{
  "title": "Alternate Interior Angles - Grade 7 CBSE",
  "total_questions": 150,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Alternate interior angles are formed when a transversal crosses:", "options": {"A": "Intersecting lines", "B": "Parallel lines", "C": "Perpendicular lines", "D": "Any two lines"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "Alternate interior angles are:", "options": {"A": "Always equal", "B": "Always supplementary", "C": "Always complementary", "D": "Always unequal"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "If two parallel lines are cut by a transversal, alternate interior angles are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Equal", "D": "Right angles"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "In the figure with parallel lines, if one alternate interior angle is 70°, the other is:", "options": {"A": "70°", "B": "110°", "C": "20°", "D": "290°"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Alternate interior angles lie on the _____ of the transversal.", "options": {"A": "Same side", "B": "Opposite sides", "C": "Right side", "D": "Left side"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Which pair of angles are alternate interior angles?", "options": {"A": "∠3 and ∠5", "B": "∠1 and ∠2", "C": "∠4 and ∠6", "D": "∠2 and ∠8"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "If lines are not parallel, alternate interior angles are:", "options": {"A": "Always equal", "B": "Never equal", "C": "Sometimes equal", "D": "Always supplementary"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Alternate interior angles are located:", "options": {"A": "Outside the parallel lines", "B": "Between the parallel lines", "C": "On the same line", "D": "At the intersection point"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "In parallel lines cut by a transversal, if ∠3 = 65°, which angle is its alternate interior angle?", "options": {"A": "∠5", "B": "∠6", "C": "∠7", "D": "∠8"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "The sum of alternate interior angles when lines are parallel is:", "options": {"A": "90°", "B": "180°", "C": "360°", "D": "Equal, not a fixed sum"}, "correct_answer": "D"},
    {"id": 11, "difficulty": "easy", "question": "If alternate interior angles are equal, the lines are:", "options": {"A": "Perpendicular", "B": "Parallel", "C": "Intersecting", "D": "Coincident"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "In the standard numbering, ∠4 and ∠6 are:", "options": {"A": "Corresponding angles", "B": "Alternate interior angles", "C": "Vertically opposite angles", "D": "Alternate exterior angles"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "If ∠2 = 110° and lines are parallel, its alternate interior angle is:", "options": {"A": "70°", "B": "110°", "C": "290°", "D": "180°"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Alternate interior angles are always:", "options": {"A": "Adjacent", "B": "Non-adjacent", "C": "On the same side", "D": "Supplementary"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "How many pairs of alternate interior angles are formed when a transversal cuts two parallel lines?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "If ∠3 and ∠5 are alternate interior angles and ∠3 = 45°, then ∠5 =", "options": {"A": "45°", "B": "135°", "C": "90°", "D": "180°"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Alternate interior angles are equal only when:", "options": {"A": "Lines are perpendicular", "B": "Lines are parallel", "C": "Lines intersect", "D": "Always"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "In parallel lines, alternate interior angles and corresponding angles are both:", "options": {"A": "Supplementary", "B": "Equal", "C": "Complementary", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "If a transversal cuts two lines and alternate interior angles are 85° each, the lines are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting at acute angle", "D": "Cannot be determined"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "∠4 and ∠6 are alternate interior angles in standard numbering. If lines are parallel and ∠4 = 60°, then ∠6 =", "options": {"A": "60°", "B": "120°", "C": "30°", "D": "90°"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "In the figure, if l || m and transversal t cuts them, with ∠3 = 75°, find ∠6.", "options": {"A": "75°", "B": "105°", "C": "15°", "D": "285°"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "If two parallel lines are cut by a transversal and one alternate interior angle is (2x + 20)° and the other is (3x - 10)°, find x.", "options": {"A": "10", "B": "20", "C": "30", "D": "40"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "In the figure, AB || CD and transversal EF cuts them at G and H. If ∠AGH = 65°, find ∠GHD.", "options": {"A": "65°", "B": "115°", "C": "25°", "D": "295°"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "If ∠1 and ∠2 are alternate interior angles with ∠1 = (4x - 15)° and ∠2 = (x + 45)°, and lines are parallel, find ∠1.", "options": {"A": "45°", "B": "55°", "C": "65°", "D": "75°"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "In the figure, if p || q and ∠3 = 110°, find its alternate interior angle.", "options": {"A": "70°", "B": "110°", "C": "290°", "D": "180°"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "If a transversal cuts two lines making alternate interior angles (5x - 20)° and (3x + 40)° equal, find x.", "options": {"A": "10", "B": "20", "C": "30", "D": "40"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "In the figure, if l || m and ∠4 = 125°, find ∠5.", "options": {"A": "55°", "B": "125°", "C": "305°", "D": "180°"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "If two lines are cut by a transversal and alternate interior angles are supplementary, the lines are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting at 60°", "D": "Cannot be determined"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "In parallel lines, if one alternate interior angle is 30° more than the other, find both angles.", "options": {"A": "30° and 60°", "B": "45° and 75°", "C": "60° and 90°", "D": "75° and 105°"}, "correct_answer": "D"},
    {"id": 30, "difficulty": "medium", "question": "If ∠3 and ∠5 are alternate interior angles with ∠3 = (7x - 10)° and ∠5 = (5x + 30)°, find x when lines are parallel.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "In the figure, AB || CD. If ∠BPQ = 50° and ∠PRD = 130°, find ∠PQR.", "options": {"A": "50°", "B": "80°", "C": "100°", "D": "130°"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "If alternate interior angles are in ratio 3:7 and lines are parallel, find the angles.", "options": {"A": "36° and 84°", "B": "45° and 105°", "C": "54° and 126°", "D": "60° and 140°"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "In the figure, if l || m and ∠1 = 70°, find ∠6.", "options": {"A": "70°", "B": "110°", "C": "20°", "D": "290°"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "If a transversal cuts two lines making alternate interior angles (2x + 25)° and (3x - 15)° equal, find the measure of each angle.", "options": {"A": "75°", "B": "85°", "C": "95°", "D": "105°"}, "correct_answer": "D"},
    {"id": 35, "difficulty": "medium", "question": "In the figure, PQ || RS. If ∠QXM = 40° and ∠MYR = 40°, what is the relationship between XM and YR?", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting", "D": "Coincident"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "If ∠4 and ∠6 are alternate interior angles with ∠4 = (5y - 10)° and ∠6 = (3y + 50)°, find y when lines are parallel.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "In the figure, if a || b and ∠1 = 55°, find ∠8.", "options": {"A": "55°", "B": "125°", "C": "235°", "D": "305°"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "If two lines are parallel and a transversal cuts them, making one alternate interior angle 15° less than twice the other, find the angles.", "options": {"A": "45° and 75°", "B": "55° and 95°", "C": "65° and 115°", "D": "75° and 135°"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "In the figure, AB || CD and EF is transversal. If ∠AEF = 60°, find ∠DFE.", "options": {"A": "60°", "B": "120°", "C": "30°", "D": "90°"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "If alternate interior angles are (x + 40)° and (2x - 20)° and they are equal, find x.", "options": {"A": "40", "B": "50", "C": "60", "D": "70"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "In the figure, l || m. If ∠3 = 115°, find ∠6.", "options": {"A": "65°", "B": "115°", "C": "245°", "D": "295°"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "If a transversal cuts two lines and alternate interior angles are 75° and 105°, the lines are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting at 30°", "D": "Cannot be determined"}, "correct_answer": "D"},
    {"id": 43, "difficulty": "medium", "question": "In the figure, if PQ || RS and ∠QPT = 30°, find ∠TSR.", "options": {"A": "30°", "B": "60°", "C": "150°", "D": "180°"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "If ∠4 and ∠6 are alternate interior angles with ∠4 = 3x + 20 and ∠6 = 5x - 40, and lines are parallel, find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "In the figure, AB || CD. If ∠BEF = 40°, find ∠EFD.", "options": {"A": "40°", "B": "140°", "C": "50°", "D": "90°"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "If two parallel lines are cut by a transversal, and one alternate interior angle is 20° more than the other, find both angles.", "options": {"A": "70° and 90°", "B": "80° and 100°", "C": "85° and 105°", "D": "90° and 110°"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "In the figure, if l || m and ∠2 = 85°, find ∠7.", "options": {"A": "85°", "B": "95°", "C": "275°", "D": "265°"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "If alternate interior angles are supplementary and each measures 90°, the lines are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting at 45°", "D": "Coincident"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "In the figure, PQ || RS. If ∠PAB = 65°, find ∠ABC if AB = BC.", "options": {"A": "65°", "B": "115°", "C": "50°", "D": "130°"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "If ∠3 and ∠5 are alternate interior angles with ∠3 = 4x - 25 and ∠5 = 2x + 35, find x when lines are parallel.", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "In the figure, if a || b and ∠1 = 48°, find ∠6.", "options": {"A": "48°", "B": "132°", "C": "42°", "D": "138°"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "If two lines are cut by a transversal and alternate interior angles are (3x + 10)° and (5x - 30)°, for what value of x are the lines parallel?", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "In the figure, AB || CD. If ∠APQ = 50° and ∠PRD = 130°, find ∠QPR.", "options": {"A": "50°", "B": "80°", "C": "100°", "D": "130°"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "If alternate interior angles are in ratio 4:5 and lines are parallel, find the angles.", "options": {"A": "60° and 75°", "B": "70° and 87.5°", "C": "80° and 100°", "D": "90° and 112.5°"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "In the figure, if l || m and ∠4 = 100°, find ∠5.", "options": {"A": "80°", "B": "100°", "C": "260°", "D": "280°"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "If a transversal cuts two parallel lines and one alternate interior angle is 35°, find its corresponding angle.", "options": {"A": "35°", "B": "145°", "C": "55°", "D": "125°"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "In the figure, PQ || RS. If ∠QXY = 60° and ∠YXS = 60°, what can you say about XY and RS?", "options": {"A": "XY || RS", "B": "XY ⟂ RS", "C": "XY intersects RS", "D": "XY = RS"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "If ∠4 and ∠6 are alternate interior angles with ∠4 = 7y - 20 and ∠6 = 3y + 60, find y when lines are parallel.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "In the figure, if a || b and ∠2 = 72°, find ∠7.", "options": {"A": "72°", "B": "108°", "C": "18°", "D": "162°"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "If two lines are parallel and a transversal cuts them, making one alternate interior angle three times the other, find the smaller angle.", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "In the figure, AB || CD and EF is transversal. If ∠BEF = 55°, find ∠EFC.", "options": {"A": "55°", "B": "125°", "C": "35°", "D": "145°"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "If alternate interior angles are (2x + 30)° and (4x - 50)° and they are equal, find x.", "options": {"A": "30", "B": "35", "C": "40", "D": "45"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "In the figure, l || m. If ∠3 = 95°, find ∠6.", "options": {"A": "85°", "B": "95°", "C": "265°", "D": "275°"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "If a transversal cuts two lines and alternate interior angles are 60° and 120°, the lines are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting at 60°", "D": "Cannot be parallel"}, "correct_answer": "D"},
    {"id": 65, "difficulty": "medium", "question": "In the figure, if PQ || RS and ∠PAB = 70°, find ∠ABS if AB = BS.", "options": {"A": "70°", "B": "110°", "C": "40°", "D": "140°"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "If ∠3 and ∠5 are alternate interior angles with ∠3 = 6x - 15 and ∠5 = 4x + 45, find x when lines are parallel.", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "In the figure, if a || b and ∠1 = 62°, find ∠6.", "options": {"A": "62°", "B": "118°", "C": "28°", "D": "152°"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "If two lines are cut by a transversal and alternate interior angles are (4x + 5)° and (6x - 25)°, for what value of x are the lines parallel?", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "In the figure, AB || CD. If ∠APQ = 45° and ∠PRD = 135°, find ∠PQR.", "options": {"A": "45°", "B": "90°", "C": "135°", "D": "180°"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "If alternate interior angles are in ratio 5:7 and lines are parallel, find the angles.", "options": {"A": "50° and 70°", "B": "60° and 84°", "C": "75° and 105°", "D": "80° and 112°"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "In the figure, if l || m and ∠4 = 115°, find ∠5.", "options": {"A": "65°", "B": "115°", "C": "245°", "D": "295°"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "If a transversal cuts two parallel lines and one alternate interior angle is 48°, find its vertically opposite angle.", "options": {"A": "48°", "B": "132°", "C": "42°", "D": "138°"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "In the figure, PQ || RS. If ∠QXM = 55° and ∠MYR = 55°, what is true about XM and YR?", "options": {"A": "XM || YR", "B": "XM ⟂ YR", "C": "XM intersects YR", "D": "XM = YR"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "If ∠4 and ∠6 are alternate interior angles with ∠4 = 8y - 30 and ∠6 = 2y + 90, find y when lines are parallel.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "In the figure, if a || b and ∠2 = 78°, find ∠7.", "options": {"A": "78°", "B": "102°", "C": "12°", "D": "168°"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "If two lines are parallel and a transversal cuts them, making one alternate interior angle 25° more than half the other, find the larger angle.", "options": {"A": "50°", "B": "75°", "C": "100°", "D": "125°"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "In the figure, AB || CD and EF is transversal. If ∠AEF = 48°, find ∠DFE.", "options": {"A": "48°", "B": "132°", "C": "42°", "D": "138°"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "If alternate interior angles are (3x + 40)° and (5x - 20)° and they are equal, find x.", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "In the figure, l || m. If ∠3 = 105°, find ∠6.", "options": {"A": "75°", "B": "105°", "C": "255°", "D": "285°"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "If a transversal cuts two lines and alternate interior angles are 85° and 95°, the lines are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting at 85°", "D": "Cannot be parallel"}, "correct_answer": "D"},

    {"id": 81, "difficulty": "hard", "question": "In the figure, AB || CD || EF. If ∠ABC = 65° and ∠CEF = 115°, find ∠BCE.", "options": {"A": "50°", "B": "65°", "C": "115°", "D": "130°"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "If a transversal cuts two parallel lines and the bisectors of a pair of alternate interior angles are drawn, prove that these bisectors are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting at 45°", "D": "Coincident"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "In the figure, l || m and p || q. If ∠1 = 70°, find ∠12.", "options": {"A": "70°", "B": "110°", "C": "140°", "D": "160°"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "If two lines are cut by a transversal and the alternate interior angles are (3x + 20)° and (5x - 40)°, and the corresponding angles are (2y + 10)° and (4y - 50)°, and lines are parallel, find x + y.", "options": {"A": "60", "B": "70", "C": "80", "D": "90"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "In the figure, AB || CD. Ray EF cuts them such that ∠BEF = ∠EFD. If ∠BEF = (2x + 30)° and ∠EFD = (3x - 20)°, find x.", "options": {"A": "40", "B": "50", "C": "60", "D": "70"}, "correct_answer": "B"},
    {"id": 86, "difficulty": "hard", "question": "Three parallel lines are cut by two transversals. If one alternate interior angle between first and second line is 55°, and corresponding angle between second and third line is 125°, find the angle between the transversals.", "options": {"A": "55°", "B": "70°", "C": "125°", "D": "180°"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "In the figure, l || m. A transversal p cuts them at A and B. The bisectors of alternate interior angles at A and B intersect at C. If ∠CAB = 40°, find ∠CBA.", "options": {"A": "40°", "B": "50°", "C": "80°", "D": "100°"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "If alternate interior angles are in the ratio 7:11 and their difference is 40°, and the lines are parallel, find the measure of the acute angle formed by the transversal with one line.", "options": {"A": "55°", "B": "70°", "C": "110°", "D": "125°"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "In the figure, AB || CD and EF || GH. If ∠AEF = 50°, ∠CHG = 130°, and ∠EFG = 80°, find ∠FGH.", "options": {"A": "50°", "B": "80°", "C": "100°", "D": "130°"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "If a transversal cuts two parallel lines and the alternate interior angles are (5x - 2y)° and (3x + 4y)°. If x:y = 2:1, find the angles.", "options": {"A": "60° each", "B": "72° each", "C": "84° each", "D": "96° each"}, "correct_answer": "B"},
    {"id": 91, "difficulty": "hard", "question": "In the figure, l || m || n. Transversal p cuts l at A, m at B, n at C. If ∠ABM = 70° and ∠BCN = 110°, find ∠MBC.", "options": {"A": "40°", "B": "70°", "C": "110°", "D": "140°"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "If the bisectors of a pair of alternate interior angles formed by a transversal with two lines are perpendicular, then the lines are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting at 45°", "D": "Cannot be determined"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "In the figure, AB || CD. Lines EF and GH are transversals. If ∠AEF = 60°, ∠EGH = 120°, and ∠CHG = 60°, find ∠EFG.", "options": {"A": "60°", "B": "90°", "C": "120°", "D": "150°"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "If alternate interior angles are (2x + 3y)° and (4x - y)° and corresponding angles are (3x + 2y)° and (5x - 2y)°, and lines are parallel, find x - y.", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "In the figure, three lines l, m, n are such that l || m. Line p cuts l, m, n at A, B, C. If alternate interior angles for l and m are 65° each, and for m and n are 115° each, find ∠ABC.", "options": {"A": "50°", "B": "65°", "C": "115°", "D": "130°"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "If a transversal cuts two parallel lines and the sum of the measures of alternate interior angles is 180°, what type of angles are they?", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Cannot be determined"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "In the figure, quadrilateral ABCD has AB || DC. Diagonals AC and BD intersect at O. If ∠ABD = 40° and ∠BDC = 40°, find ∠AOB.", "options": {"A": "40°", "B": "80°", "C": "100°", "D": "140°"}, "correct_answer": "C"},
    {"id": 98, "difficulty": "hard", "question": "If the alternate interior angles formed by a transversal with two lines are (3x + 2y)° and (5x - 4y)°, and the lines are parallel with x + y = 30, find the angles.", "options": {"A": "60°", "B": "75°", "C": "90°", "D": "105°"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "In the figure, l || m. Transversal p makes an angle of 55° with l. Another transversal q makes an angle of 125° with m. Find the acute angle between p and q.", "options": {"A": "55°", "B": "70°", "C": "125°", "D": "180°"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "If the bisectors of alternate interior angles include an angle of 60° with each other, and the original lines are parallel, find the measure of the alternate interior angles.", "options": {"A": "30°", "B": "60°", "C": "120°", "D": "150°"}, "correct_answer": "C"}
  ,
 {"id":101,"difficulty":"easy","question":"Alternate interior angles are equal when a transversal cuts two ____ lines.","options":{"A":"Intersecting","B":"Parallel","C":"Perpendicular","D":"Curved"},"correct_answer":"B"},
    {"id":102,"difficulty":"easy","question":"If one alternate interior angle is 48°, the other is:","options":{"A":"48°","B":"132°","C":"90°","D":"180°"},"correct_answer":"A"},
    {"id":103,"difficulty":"easy","question":"Alternate interior angles lie between the two lines and on ____ sides of the transversal.","options":{"A":"Same","B":"Adjacent","C":"Opposite","D":"Equal"},"correct_answer":"C"},
    {"id":104,"difficulty":"easy","question":"When alternate interior angles are equal, the lines are:","options":{"A":"Intersecting","B":"Parallel","C":"Perpendicular","D":"Coincident"},"correct_answer":"B"},
    {"id":105,"difficulty":"easy","question":"How many pairs of alternate interior angles are formed by one transversal?","options":{"A":"1","B":"2","C":"3","D":"4"},"correct_answer":"B"},
    {"id":106,"difficulty":"easy","question":"If ∠A = 90° and it is alternate interior to ∠B, then ∠B =","options":{"A":"45°","B":"90°","C":"135°","D":"180°"},"correct_answer":"B"},
    {"id":107,"difficulty":"easy","question":"Alternate interior angles are formed only when lines are:","options":{"A":"Parallel","B":"Intersecting","C":"Skew","D":"Horizontal"},"correct_answer":"A"},
    {"id":108,"difficulty":"easy","question":"Which angles become equal in parallel lines cut by a transversal?","options":{"A":"Interior angles","B":"Alternate interior angles","C":"Linear angles","D":"Reflex angles"},"correct_answer":"B"},
    {"id":109,"difficulty":"easy","question":"If ∠3 = 65° and ∠3 and ∠5 are alternate interior angles, ∠5 equals:","options":{"A":"65°","B":"115°","C":"35°","D":"145°"},"correct_answer":"A"},
    {"id":110,"difficulty":"easy","question":"Alternate interior angles are always:","options":{"A":"Adjacent","B":"Supplementary","C":"Equal","D":"Reflex"},"correct_answer":"C"},

    {"id":111,"difficulty":"medium","question":"Two parallel lines are cut by a transversal. If one alternate interior angle is 72°, find the other.","options":{"A":"72°","B":"108°","C":"36°","D":"180°"},"correct_answer":"A"},
    {"id":112,"difficulty":"medium","question":"If alternate interior angles are (3x + 15)° and (5x − 25)°, find x.","options":{"A":"5","B":"10","C":"15","D":"20"},"correct_answer":"B"},
    {"id":113,"difficulty":"medium","question":"If alternate interior angles are equal, what can be concluded about the lines?","options":{"A":"They intersect","B":"They are parallel","C":"They are perpendicular","D":"No conclusion"},"correct_answer":"B"},
    {"id":114,"difficulty":"medium","question":"In parallel lines, if one alternate interior angle is 40° more than the other, find both angles.","options":{"A":"70° and 110°","B":"60° and 100°","C":"80° and 120°","D":"90° and 130°"},"correct_answer":"A"},
    {"id":115,"difficulty":"medium","question":"Alternate interior angles are equal because they are formed by:","options":{"A":"Parallel lines","B":"Intersecting lines","C":"Perpendicular lines","D":"Skew lines"},"correct_answer":"A"},
    {"id":116,"difficulty":"medium","question":"If alternate interior angles are (x + 30)° and (2x − 10)°, find x.","options":{"A":"20","B":"30","C":"40","D":"50"},"correct_answer":"B"},
    {"id":117,"difficulty":"medium","question":"If one alternate interior angle is obtuse, the other is:","options":{"A":"Acute","B":"Right","C":"Obtuse","D":"Straight"},"correct_answer":"C"},
    {"id":118,"difficulty":"medium","question":"In two parallel lines cut by a transversal, alternate interior angles are equal to:","options":{"A":"Corresponding angles","B":"Linear angles","C":"Reflex angles","D":"Exterior angles only"},"correct_answer":"A"},
    {"id":119,"difficulty":"medium","question":"If alternate interior angles are 3x° and 5x°, and lines are parallel, find x.","options":{"A":"0","B":"30","C":"45","D":"Impossible"},"correct_answer":"D"},
    {"id":120,"difficulty":"medium","question":"Which condition proves two lines are parallel?","options":{"A":"Corresponding angles unequal","B":"Alternate interior angles equal","C":"Interior angles unequal","D":"Vertical angles equal"},"correct_answer":"B"},

    {"id":121,"difficulty":"medium","question":"If alternate interior angles are (4x − 20)° and (2x + 40)°, find each angle.","options":{"A":"60°","B":"70°","C":"80°","D":"90°"},"correct_answer":"C"},
    {"id":122,"difficulty":"medium","question":"When alternate interior angles are equal, the transversal is said to cut the lines at:","options":{"A":"Right angles","B":"Equal angles","C":"Parallel condition","D":"Supplementary angles"},"correct_answer":"C"},
    {"id":123,"difficulty":"medium","question":"If ∠A = 110° and ∠A is alternate interior to ∠B, find ∠B.","options":{"A":"70°","B":"110°","C":"180°","D":"90°"},"correct_answer":"B"},
    {"id":124,"difficulty":"medium","question":"Alternate interior angles are formed on the inside of the two lines and on ____ sides of the transversal.","options":{"A":"Same","B":"Adjacent","C":"Opposite","D":"Equal"},"correct_answer":"C"},
    {"id":125,"difficulty":"medium","question":"If alternate interior angles are 65° each, what is the measure of the corresponding angle?","options":{"A":"65°","B":"115°","C":"35°","D":"180°"},"correct_answer":"A"},
    {"id":126,"difficulty":"medium","question":"Alternate interior angles can be used to test whether lines are:","options":{"A":"Intersecting","B":"Parallel","C":"Perpendicular","D":"Skew"},"correct_answer":"B"},
    {"id":127,"difficulty":"medium","question":"If one alternate interior angle is reflex, the other is:","options":{"A":"Acute","B":"Obtuse","C":"Reflex","D":"Right"},"correct_answer":"C"},
    {"id":128,"difficulty":"medium","question":"If alternate interior angles are equal, the sum of interior angles on the same side is:","options":{"A":"90°","B":"180°","C":"360°","D":"Equal"},"correct_answer":"B"},
    {"id":129,"difficulty":"medium","question":"If alternate interior angles are equal, what is the relation between the two lines?","options":{"A":"Coincident","B":"Parallel","C":"Intersecting","D":"Skew"},"correct_answer":"B"},
    {"id":130,"difficulty":"medium","question":"Which angle pair confirms parallelism of lines?","options":{"A":"Vertical angles","B":"Adjacent angles","C":"Alternate interior angles","D":"Reflex angles"},"correct_answer":"C"},

    {"id":131,"difficulty":"hard","question":"If alternate interior angles are in the ratio 2:3 and lines are parallel, find the angles.","options":{"A":"72° and 108°","B":"60° and 120°","C":"54° and 81°","D":"90° and 135°"},"correct_answer":"A"},
    {"id":132,"difficulty":"hard","question":"A transversal cuts two lines such that alternate interior angles are (3x + 10)° and (5x − 30)°. Find x.","options":{"A":"10","B":"15","C":"20","D":"25"},"correct_answer":"C"},
    {"id":133,"difficulty":"hard","question":"If alternate interior angles are equal and measure 75°, find the obtuse angle formed at the intersection.","options":{"A":"75°","B":"105°","C":"150°","D":"180°"},"correct_answer":"B"},
    {"id":134,"difficulty":"hard","question":"If alternate interior angles are (x + 20)° and (3x − 40)°, find x.","options":{"A":"20","B":"30","C":"40","D":"50"},"correct_answer":"B"},
    {"id":135,"difficulty":"hard","question":"If alternate interior angles are equal and one is acute, the other must be:","options":{"A":"Obtuse","B":"Right","C":"Acute","D":"Reflex"},"correct_answer":"C"},
    {"id":136,"difficulty":"hard","question":"If alternate interior angles are each 90°, what is the angle between the transversal and each line?","options":{"A":"45°","B":"60°","C":"90°","D":"120°"},"correct_answer":"C"},
    {"id":137,"difficulty":"hard","question":"If alternate interior angles are in ratio 5:7 and differ by 20°, find the smaller angle.","options":{"A":"50°","B":"60°","C":"70°","D":"80°"},"correct_answer":"B"},
    {"id":138,"difficulty":"hard","question":"If alternate interior angles are equal, then the interior angles on the same side are:","options":{"A":"Equal","B":"Supplementary","C":"Complementary","D":"Reflex"},"correct_answer":"B"},
    {"id":139,"difficulty":"hard","question":"If alternate interior angles are each x° and corresponding angles are (x + 20)°, find x.","options":{"A":"40","B":"50","C":"60","D":"70"},"correct_answer":"C"},
    {"id":140,"difficulty":"hard","question":"If alternate interior angles are equal and one interior angle is 140°, find the acute angle formed.","options":{"A":"40°","B":"50°","C":"60°","D":"70°"},"correct_answer":"A"},

    {"id":141,"difficulty":"hard","question":"If two transversals cut parallel lines making alternate interior angles 50° and 130°, find the acute angle between the transversals.","options":{"A":"30°","B":"40°","C":"50°","D":"60°"},"correct_answer":"B"},
    {"id":142,"difficulty":"hard","question":"If alternate interior angles are equal and one exterior angle is 110°, find the alternate interior angle.","options":{"A":"70°","B":"110°","C":"55°","D":"90°"},"correct_answer":"B"},
    {"id":143,"difficulty":"hard","question":"Alternate interior angles are equal only if the lines are:","options":{"A":"Intersecting","B":"Parallel","C":"Perpendicular","D":"Skew"},"correct_answer":"B"},
    {"id":144,"difficulty":"hard","question":"If alternate interior angles are (2x + 10)° and (4x − 50)°, find the angle value.","options":{"A":"60°","B":"70°","C":"80°","D":"90°"},"correct_answer":"C"},
    {"id":145,"difficulty":"hard","question":"If alternate interior angles are equal and one angle is reflex, the other is:","options":{"A":"Acute","B":"Obtuse","C":"Reflex","D":"Right"},"correct_answer":"C"},
    {"id":146,"difficulty":"hard","question":"If alternate interior angles are equal and sum to 180°, find each angle.","options":{"A":"60°","B":"90°","C":"120°","D":"150°"},"correct_answer":"B"},
    {"id":147,"difficulty":"hard","question":"If alternate interior angles are equal and the transversal is perpendicular to one line, then the other line is:","options":{"A":"Parallel","B":"Perpendicular","C":"Intersecting","D":"Skew"},"correct_answer":"B"},
    {"id":148,"difficulty":"hard","question":"If alternate interior angles are equal and each is 135°, find the acute angle formed.","options":{"A":"45°","B":"55°","C":"65°","D":"75°"},"correct_answer":"A"},
    {"id":149,"difficulty":"hard","question":"If alternate interior angles are equal and one corresponding angle is 65°, find the alternate interior angle.","options":{"A":"65°","B":"115°","C":"45°","D":"180°"},"correct_answer":"A"},
    {"id":150,"difficulty":"hard","question":"Alternate interior angles help in identifying whether two lines are:","options":{"A":"Intersecting","B":"Parallel","C":"Perpendicular","D":"Skew"},"correct_answer":"B"}
]
}