{
  "title": "Alternate Interior Angles - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "If two parallel lines are cut by a transversal, alternate interior angles are:", "options": {"A": "Supplementary", "B": "Complementary", "C": "Equal", "D": "Right angles"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "If ∠1 and ∠2 are alternate interior angles, and ∠1 = 60°, what is ∠2?", "options": {"A": "120°", "B": "30°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "Which angles are always equal when lines are parallel?", "options": {"A": "Corresponding angles", "B": "Linear pair", "C": "Adjacent angles", "D": "Vertical angles"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "If lines are not parallel, alternate interior angles are:", "options": {"A": "Always equal", "B": "Sometimes equal", "C": "Never equal", "D": "Always supplementary"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "Alternate interior angles are located:", "options": {"A": "On same side of transversal", "B": "Opposite sides of transversal", "C": "Outside parallel lines", "D": "Adjacent to each other"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "If ∠3 = 45° and it's an alternate interior angle to ∠4, what is ∠4?", "options": {"A": "45°", "B": "135°", "C": "90°", "D": "180°"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "How many pairs of alternate interior angles are formed by a transversal cutting two lines?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "If two lines are parallel, alternate interior angles are:", "options": {"A": "Congruent", "B": "Supplementary", "C": "Complementary", "D": "Acute"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Which theorem proves alternate interior angles are equal?", "options": {"A": "Vertical angles theorem", "B": "Corresponding angles postulate", "C": "Linear pair postulate", "D": "Angle sum property"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "If ∠A and ∠B are alternate interior angles and lines are parallel, then:", "options": {"A": "∠A + ∠B = 90°", "B": "∠A + ∠B = 180°", "C": "∠A = ∠B", "D": "∠A = 180° - ∠B"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "Alternate interior angles are always:", "options": {"A": "On the interior of parallel lines", "B": "On the exterior of parallel lines", "C": "Equal to exterior angles", "D": "Obtuse angles"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "If two lines are cut by a transversal and alternate interior angles are equal, then lines are:", "options": {"A": "Perpendicular", "B": "Parallel", "C": "Intersecting", "D": "Coincident"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "Which angle pair is NOT formed by a transversal?", "options": {"A": "Alternate interior", "B": "Vertical", "C": "Corresponding", "D": "Same-side interior"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "If ∠P = 70° and it's alternate interior to ∠Q, what is ∠Q?", "options": {"A": "110°", "B": "70°", "C": "20°", "D": "160°"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "Alternate interior angles are equal only when:", "options": {"A": "Lines intersect", "B": "Lines are parallel", "C": "Lines are perpendicular", "D": "Always"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "Which statement is true about alternate interior angles?", "options": {"A": "They add to 90°", "B": "They are always acute", "C": "They are non-adjacent", "D": "They form a straight line"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "If lines are parallel, alternate interior angles and corresponding angles are both:", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "How can you prove lines are parallel?", "options": {"A": "Show alternate interior angles are equal", "B": "Show vertical angles are equal", "C": "Show adjacent angles are equal", "D": "Show linear pair sums to 180°"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "If ∠X and ∠Y are alternate interior angles and ∠X = 85°, what is ∠Y if lines are parallel?", "options": {"A": "85°", "B": "95°", "C": "5°", "D": "175°"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Which diagram shows alternate interior angles?", "options": {"A": "Angles on same side of transversal", "B": "Angles between parallel lines on opposite sides", "C": "Angles outside parallel lines", "D": "Angles sharing a vertex"}, "correct_answer": "B"},
    
    {"id": 21, "difficulty": "medium", "question": "In the figure, l || m and transversal t cuts them. If one alternate interior angle is (3x - 10)° and the other is (2x + 20)°, find x.", "options": {"A": "10", "B": "20", "C": "30", "D": "40"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "If AB || CD and transversal EF cuts them at G and H respectively. If ∠AGE = 65°, find ∠GHD.", "options": {"A": "65°", "B": "115°", "C": "25°", "D": "295°"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Two parallel lines are cut by a transversal. If one alternate interior angle is 5 times its supplement, find the angle.", "options": {"A": "30°", "B": "150°", "C": "36°", "D": "144°"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "In parallelogram ABCD, AB || DC and AD || BC. If ∠A = 70°, find ∠C using alternate interior angles.", "options": {"A": "70°", "B": "110°", "C": "20°", "D": "160°"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "If PQ || RS and transversal XY cuts them. If one alternate interior angle is (4x + 15)° and the other is (5x - 5)°, find both angles.", "options": {"A": "75°, 75°", "B": "95°, 95°", "C": "85°, 85°", "D": "105°, 105°"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Two lines are cut by a transversal forming alternate interior angles measuring (2x + 30)° and (4x - 20)°. If the lines are parallel, find x.", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "In the figure, if a || b and c is transversal, ∠1 = 120°. Find the alternate interior angle to ∠1.", "options": {"A": "60°", "B": "120°", "C": "30°", "D": "150°"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "If alternate interior angles are (7x - 10)° and (5x + 20)° and lines are parallel, what is the measure of each angle?", "options": {"A": "85°", "B": "95°", "C": "105°", "D": "115°"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "In trapezium ABCD with AB || DC, if ∠A = 65°, find ∠D using alternate interior angles concept.", "options": {"A": "65°", "B": "115°", "C": "25°", "D": "295°"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Two parallel lines are cut by a transversal. If one alternate interior angle is 20° more than half of the other, find the angles.", "options": {"A": "60°, 60°", "B": "80°, 80°", "C": "100°, 100°", "D": "120°, 120°"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "If LM || NO and transversal PQ makes an angle of 55° with LM, what angle does it make with NO on the alternate interior side?", "options": {"A": "55°", "B": "125°", "C": "35°", "D": "145°"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "In rectangle ABCD, AB || DC. If ∠ABD = 40°, find ∠BDC using alternate interior angles.", "options": {"A": "40°", "B": "50°", "C": "90°", "D": "140°"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Two lines are cut by a transversal. The alternate interior angles are in ratio 4:5. If lines are parallel, find the angles.", "options": {"A": "80°, 100°", "B": "72°, 90°", "C": "60°, 75°", "D": "96°, 120°"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "If a transversal cuts two parallel lines, and one alternate interior angle is 30° less than twice the other, find both angles.", "options": {"A": "50°, 50°", "B": "60°, 60°", "C": "70°, 70°", "D": "80°, 80°"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "In the figure, if line m || n and p is transversal, and ∠2 = 110°, find the alternate interior angle to ∠2.", "options": {"A": "70°", "B": "110°", "C": "20°", "D": "160°"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Two parallel lines are cut by a transversal. If one alternate interior angle measures (x² - 10)° and the other measures (3x + 40)°, find x.", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "If lines are parallel and alternate interior angles differ by 40°, find the angles.", "options": {"A": "70°, 110°", "B": "60°, 100°", "C": "50°, 90°", "D": "40°, 80°"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "In triangle ABC, DE || BC with D on AB and E on AC. If ∠ADE = 50°, find ∠ABC using alternate interior angles.", "options": {"A": "50°", "B": "130°", "C": "40°", "D": "140°"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Two lines are cut by a transversal. If alternate interior angles are (5x - 20)° and (3x + 40)° and lines are parallel, find x.", "options": {"A": "10", "B": "20", "C": "30", "D": "40"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "If a || b and c is transversal, and one alternate interior angle is 15° more than three-fifths of the other, find the angles.", "options": {"A": "75°, 75°", "B": "80°, 80°", "C": "85°, 85°", "D": "90°, 90°"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "In the figure, PQ || RS. If ∠PAB = 65° and ∠ABS = 115°, which angles are alternate interior?", "options": {"A": "∠PAB and ∠ABC", "B": "∠PAB and ∠ABS", "C": "∠PAB and ∠BAS", "D": "∠PAB and ∠RBA"}, "correct_answer": "D"},
    {"id": 42, "difficulty": "medium", "question": "Two parallel lines are cut by a transversal. If one alternate interior angle is (x + 30)° and the other is (2x - 20)°, find x.", "options": {"A": "30", "B": "40", "C": "50", "D": "60"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "medium", "question": "If lines l and m are parallel and transversal t makes ∠1 = 75° with l, what is the alternate interior angle on m?", "options": {"A": "75°", "B": "105°", "C": "15°", "D": "165°"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "In rhombus ABCD, AB || DC. If ∠BAC = 35°, find ∠ACD using alternate interior angles.", "options": {"A": "35°", "B": "55°", "C": "70°", "D": "145°"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Two lines are cut by a transversal. Alternate interior angles are equal and each is 20° more than one-third of a right angle. Find the angles.", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "medium", "question": "If a || b, and transversal c makes angles (3x + 10)° and (5x - 30)° as alternate interior angles, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "In the figure, if AB || CD and EF is transversal, ∠BEF = 110°. Find the alternate interior angle to ∠BEF.", "options": {"A": "70°", "B": "110°", "C": "20°", "D": "160°"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "Two parallel lines are cut by a transversal. If alternate interior angles are in ratio 7:8, find each angle.", "options": {"A": "70°, 80°", "B": "84°, 96°", "C": "77°, 88°", "D": "91°, 104°"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "If lines are parallel and one alternate interior angle is 10° less than twice the other, find both angles.", "options": {"A": "60°, 60°", "B": "70°, 70°", "C": "80°, 80°", "D": "90°, 90°"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "In triangle ABC, if DE || BC, and ∠ADE = (2x + 10)°, ∠ABC = (3x - 20)°, find x.", "options": {"A": "20", "B": "30", "C": "40", "D": "50"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Two lines are cut by a transversal. If alternate interior angles are (4x - 15)° and (2x + 35)° and lines are parallel, find each angle.", "options": {"A": "65°", "B": "75°", "C": "85°", "D": "95°"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "If l || m, and transversal t makes ∠1 = (5x + 20)° with l and ∠2 = (7x - 10)° with m as alternate interior angles, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "In parallelogram ABCD, AB || DC. If ∠DAB = 60°, find ∠BCD using alternate interior angles.", "options": {"A": "60°", "B": "120°", "C": "30°", "D": "150°"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Two parallel lines are cut by a transversal. If one alternate interior angle is 30° more than half the other, find both equal angles.", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "If a || b and c is transversal, and alternate interior angles are (x² + 10)° and (4x + 55)°, find x.", "options": {"A": "5", "B": "9", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "In the figure, PQ || RS. If ∠QPT = 40° and ∠TSR = 140°, find alternate interior angle to ∠QPT.", "options": {"A": "40°", "B": "140°", "C": "50°", "D": "130°"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Two lines are cut by a transversal. Alternate interior angles measure (3x + 20)° and (5x - 40)°. If lines are parallel, find x.", "options": {"A": "20", "B": "30", "C": "40", "D": "50"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "medium", "question": "If lines are parallel and alternate interior angles are supplementary, what is each angle?", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "180°"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "In trapezium ABCD with AB || DC, if ∠A = 80°, find ∠D using alternate interior angles.", "options": {"A": "80°", "B": "100°", "C": "10°", "D": "170°"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Two parallel lines are cut by a transversal. If one alternate interior angle is (2x + 50)° and the other is (3x + 10)°, find x.", "options": {"A": "30", "B": "40", "C": "50", "D": "60"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "If LM || NO, and transversal PQ makes ∠LMP = 72°, find alternate interior angle on line NO.", "options": {"A": "72°", "B": "108°", "C": "18°", "D": "162°"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "In rectangle PQRS, PQ || SR. If ∠PQS = 55°, find ∠QSR using alternate interior angles.", "options": {"A": "55°", "B": "125°", "C": "35°", "D": "145°"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Two lines are cut by a transversal. Alternate interior angles are in ratio 3:4. If lines are parallel, find each angle.", "options": {"A": "60°, 80°", "B": "72°, 96°", "C": "75°, 100°", "D": "77°, 103°"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "If a transversal cuts two parallel lines, and one alternate interior angle is 40° less than three times the other, find both angles.", "options": {"A": "55°, 55°", "B": "60°, 60°", "C": "65°, 65°", "D": "70°, 70°"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "In the figure, if a || b and c is transversal, and ∠1 = 135°, find alternate interior angle to ∠1.", "options": {"A": "45°", "B": "135°", "C": "35°", "D": "155°"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "Two parallel lines are cut by a transversal. If one alternate interior angle measures (x² - 5)° and the other measures (4x + 35)°, find x.", "options": {"A": "4", "B": "8", "C": "10", "D": "12"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "If lines are parallel and alternate interior angles differ by 30°, find the angles.", "options": {"A": "75°, 105°", "B": "70°, 100°", "C": "65°, 95°", "D": "60°, 90°"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "In triangle ABC, DE || BC with D on AB. If ∠ADE = 65°, find ∠ABC.", "options": {"A": "65°", "B": "115°", "C": "25°", "D": "295°"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Two lines are cut by a transversal. If alternate interior angles are (6x - 10)° and (4x + 30)° and lines are parallel, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "If a || b and c is transversal, and one alternate interior angle is 25° more than two-fifths of the other, find both equal angles.", "options": {"A": "75°", "B": "85°", "C": "95°", "D": "105°"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "In the figure, AB || CD. If ∠APQ = 120° and ∠PQD = 60°, which angles are alternate interior?", "options": {"A": "∠APQ and ∠PQR", "B": "∠APQ and ∠PQD", "C": "∠APQ and ∠QPC", "D": "∠APQ and ∠RQD"}, "correct_answer": "D"},
    {"id": 72, "difficulty": "medium", "question": "Two parallel lines are cut by a transversal. If one alternate interior angle is (x + 40)° and the other is (3x - 20)°, find x.", "options": {"A": "20", "B": "30", "C": "40", "D": "50"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "If lines l and m are parallel and transversal t makes ∠1 = 48° with l, what is alternate interior angle on m?", "options": {"A": "48°", "B": "132°", "C": "42°", "D": "138°"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "In rhombus PQRS, PQ || SR. If ∠QPR = 40°, find ∠PRS using alternate interior angles.", "options": {"A": "40°", "B": "50°", "C": "80°", "D": "140°"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Two lines are cut by a transversal. Alternate interior angles are equal and each is 15° more than one-fourth of 180°. Find angles.", "options": {"A": "45°", "B": "60°", "C": "75°", "D": "90°"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "If a || b, and transversal c makes angles (2x + 25)° and (5x - 20)° as alternate interior angles, find x.", "options": {"A": "12", "B": "15", "C": "18", "D": "21"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "In the figure, if PQ || RS and TU is transversal, ∠QTU = 95°. Find alternate interior angle to ∠QTU.", "options": {"A": "85°", "B": "95°", "C": "5°", "D": "175°"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "Two parallel lines are cut by a transversal. Alternate interior angles are in ratio 5:7. Find each angle.", "options": {"A": "75°, 105°", "B": "65°, 91°", "C": "70°, 98°", "D": "80°, 112°"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "If lines are parallel and one alternate interior angle is 15° more than 1.5 times the other, find both angles.", "options": {"A": "60°, 60°", "B": "70°, 70°", "C": "80°, 80°", "D": "90°, 90°"}, "correct_answer": "D"},
    {"id": 80, "difficulty": "medium", "question": "In triangle XYZ, if ST || YZ, and ∠XST = (4x - 15)°, ∠XYZ = (3x + 25)°, find x.", "options": {"A": "30", "B": "35", "C": "40", "D": "45"}, "correct_answer": "C"},
    
    {"id": 81, "difficulty": "hard", "question": "In a parallelogram ABCD, AB || DC and AD || BC. If ∠A = (3x + 10)° and ∠C = (5x - 30)°, find x using alternate interior angles concept.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Two parallel lines are cut by a transversal. If one alternate interior angle is 20° less than three times its complement, find the angle.", "options": {"A": "50°", "B": "65°", "C": "70°", "D": "75°"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "In triangle ABC, DE || BC, D on AB, E on AC. If ∠ADE = (2x² - 10)° and ∠ABC = (x² + 3x + 20)°, find x.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "If lines l and m are parallel, and transversal p makes angles (x² + 2x)° and (3x² - 4x)° as alternate interior angles, find all possible values of x.", "options": {"A": "0, 3", "B": "0, 4", "C": "0, 5", "D": "0, 6"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "In a trapezium ABCD with AB || DC, if ∠A = (4x - 20)° and ∠D = (6x - 80)°, find x using alternate interior angles.", "options": {"A": "30", "B": "40", "C": "50", "D": "60"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "Two lines are cut by a transversal. If alternate interior angles are (x³ - 8)° and (x² + 2x + 4)° and lines are parallel, find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "In the figure, if AB || CD || EF, and transversal GH cuts them. If ∠1 = 65° and ∠2 = 115°, find all alternate interior angles relationships.", "options": {"A": "∠1 = ∠3, ∠2 = ∠4", "B": "∠1 = ∠4, ∠2 = ∠3", "C": "∠1 = ∠2, ∠3 = ∠4", "D": "∠1 + ∠3 = 180°, ∠2 + ∠4 = 180°"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "If three parallel lines are cut by two transversals making alternate interior angles (2x + 15)°, (3x - 5)°, and (x + 25)° respectively, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 89, "difficulty": "hard", "question": "In parallelogram PQRS, if PQ || SR and PS || QR, and ∠P = (5x - 10)°, ∠R = (3x + 50)°, find x using alternate interior angles in two different ways.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "Two lines are cut by a transversal. If alternate interior angles satisfy the equation 2∠A + 3∠B = 360° and lines are parallel, find ∠A and ∠B.", "options": {"A": "72°, 72°", "B": "60°, 80°", "C": "90°, 60°", "D": "80°, 80°"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "In triangle ABC, if D and E are points on AB and AC such that DE || BC, and ∠ADE = (x² + 10)°, ∠ABC = (4x + 25)°, find all possible x values.", "options": {"A": "3, 5", "B": "4, 5", "C": "5, 7", "D": "6, 8"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "If lines are parallel and alternate interior angles are such that one angle's measure is the arithmetic mean of 50° and 130°, find both angles.", "options": {"A": "70°, 70°", "B": "80°, 80°", "C": "90°, 90°", "D": "100°, 100°"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "In the figure, AB || CD and EF || GH. If ∠1 = 75° and ∠2 = 105°, find all alternate interior angles and their measures.", "options": {"A": "∠1 = ∠3 = 75°, ∠2 = ∠4 = 105°", "B": "∠1 = ∠4 = 75°, ∠2 = ∠3 = 105°", "C": "∠1 = ∠2 = 75°, ∠3 = ∠4 = 105°", "D": "∠1 = 75°, ∠2 = 105°, ∠3 = 75°, ∠4 = 75°"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Two parallel lines are cut by a transversal. If alternate interior angles are in the ratio (√2 + 1):(√2 - 1), find the angles.", "options": {"A": "67.5°, 22.5°", "B": "75°, 15°", "C": "72°, 18°", "D": "80°, 10°"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "In a complex figure with multiple parallel lines and transversals, if ∠1 = 40°, ∠2 = 140°, ∠3 = 40°, ∠4 = 140°, identify all pairs of alternate interior angles.", "options": {"A": "∠1 & ∠3, ∠2 & ∠4", "B": "∠1 & ∠4, ∠2 & ∠3", "C": "∠1 & ∠2, ∠3 & ∠4", "D": "All angles are alternate interior"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "If lines l || m and transversal p makes angles with measures forming an arithmetic progression with common difference 10°, find all alternate interior angles.", "options": {"A": "50°, 50°, 70°, 70°", "B": "60°, 60°, 80°, 80°", "C": "70°, 70°, 90°, 90°", "D": "80°, 80°, 100°, 100°"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "In quadrilateral ABCD with AB || DC and AD || BC, if ∠A = (2x² - 5x)° and ∠C = (x² + 15x)°, find x.", "options": {"A": "0, 10", "B": "0, 15", "C": "0, 20", "D": "0, 25"}, "correct_answer": "C"},
    {"id": 98, "difficulty": "hard", "question": "Two lines are cut by a transversal. If alternate interior angles satisfy sin(∠A) = cos(∠B) and lines are parallel, find ∠A and ∠B.", "options": {"A": "45°, 45°", "B": "30°, 60°", "C": "60°, 30°", "D": "90°, 0°"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "In the figure with three parallel lines cut by two transversals, if ∠1 = (3x + 20)°, ∠2 = (5x - 40)°, ∠3 = (4x - 10)°, and all corresponding angles are equal, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "D"},
    {"id": 100, "difficulty": "hard", "question": "If alternate interior angles are such that their measures in degrees are consecutive integers whose product is 506, find the angles.", "options": {"A": "22°, 23°", "B": "21°, 22°", "C": "23°, 22°", "D": "22°, 22°"}, "correct_answer": "A"}
  ]
}