{
  "title": "Corresponding Angles - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "If two parallel lines are cut by a transversal, corresponding angles are:", "options": {"A": "Supplementary", "B": "Complementary", "C": "Equal", "D": "Right angles"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "Corresponding angles are located:", "options": {"A": "On same side of transversal", "B": "Opposite sides of transversal", "C": "In same relative position", "D": "Adjacent to each other"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "If ∠1 = 45° and it's corresponding to ∠2, what is ∠2 if lines are parallel?", "options": {"A": "45°", "B": "135°", "C": "90°", "D": "180°"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "How many pairs of corresponding angles are formed by a transversal?", "options": {"A": "2", "B": "3", "C": "4", "D": "6"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "If lines are not parallel, corresponding angles are:", "options": {"A": "Always equal", "B": "Sometimes equal", "C": "Never equal", "D": "Always supplementary"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "Corresponding angles postulate states that if lines are parallel, then:", "options": {"A": "Alternate interior angles are equal", "B": "Corresponding angles are equal", "C": "Same side interior are supplementary", "D": "Vertical angles are equal"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "If ∠3 = 60° and corresponds to ∠4, and lines are parallel, ∠4 = ?", "options": {"A": "30°", "B": "60°", "C": "120°", "D": "180°"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "Corresponding angles are always:", "options": {"A": "On same side of transversal", "B": "In matching corners", "C": "Inside parallel lines", "D": "Outside parallel lines"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "If corresponding angles are equal, then lines are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting", "D": "Coincident"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Which is NOT a pair of corresponding angles?", "options": {"A": "∠1 and ∠5", "B": "∠2 and ∠6", "C": "∠3 and ∠7", "D": "∠4 and ∠5"}, "correct_answer": "D"},
    {"id": 11, "difficulty": "easy", "question": "If lines are parallel, corresponding angles and alternate interior angles are both:", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Corresponding angles are used to prove:", "options": {"A": "Lines are parallel", "B": "Lines are perpendicular", "C": "Angles are acute", "D": "Triangle sum property"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "If ∠A = 75° and corresponds to ∠B with parallel lines, ∠B = ?", "options": {"A": "15°", "B": "75°", "C": "105°", "D": "165°"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "In standard labeling, which angles correspond?", "options": {"A": "∠1 and ∠3", "B": "∠2 and ∠4", "C": "∠1 and ∠5", "D": "∠3 and ∠6"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "If a transversal cuts two lines and corresponding angles are equal, lines must be:", "options": {"A": "In same plane", "B": "Parallel", "C": "Perpendicular", "D": "Intersecting"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "Corresponding angles are always:", "options": {"A": "Adjacent", "B": "Non-adjacent", "C": "Form linear pair", "D": "Equal to vertical angles"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "If ∠P = 85° and it's corresponding angle, and lines are parallel, what is corresponding angle?", "options": {"A": "85°", "B": "95°", "C": "5°", "D": "175°"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Which theorem is converse of corresponding angles postulate?", "options": {"A": "If corresponding angles equal, lines parallel", "B": "If alternate interior equal, lines parallel", "C": "If same side interior supplementary, lines parallel", "D": "If vertical angles equal, lines parallel"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "In diagram with parallel lines, if ∠1 = 40°, then ∠5 = ?", "options": {"A": "40°", "B": "50°", "C": "140°", "D": "180°"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Corresponding angles are equal only when:", "options": {"A": "Lines intersect", "B": "Lines are parallel", "C": "Lines are perpendicular", "D": "Always"}, "correct_answer": "B"},
    
    {"id": 21, "difficulty": "medium", "question": "If l || m and transversal t cuts them, and one corresponding angle is (3x + 20)° and other is (5x - 40)°, find x.", "options": {"A": "20", "B": "30", "C": "40", "D": "50"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "In figure, AB || CD and transversal EF. If ∠AEF = 70°, find corresponding angle at C.", "options": {"A": "70°", "B": "110°", "C": "20°", "D": "160°"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one corresponding angle is 4 times its supplement, find the angle.", "options": {"A": "36°", "B": "144°", "C": "72°", "D": "108°"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "In parallelogram ABCD, AB || DC. If ∠DAB = 65°, find corresponding angle at C.", "options": {"A": "65°", "B": "115°", "C": "25°", "D": "295°"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "If PQ || RS and transversal XY, and corresponding angles are (4x + 10)° and (6x - 20)°, find both angles.", "options": {"A": "70°, 70°", "B": "80°, 80°", "C": "90°, 90°", "D": "100°, 100°"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "Two lines cut by transversal. Corresponding angles are (3x + 15)° and (5x - 25)°. If lines parallel, find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "In figure, a || b and c is transversal. If ∠1 = 110°, find corresponding angle to ∠1.", "options": {"A": "70°", "B": "110°", "C": "20°", "D": "160°"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "If corresponding angles are (8x - 10)° and (6x + 30)° and lines parallel, find each angle.", "options": {"A": "110°", "B": "120°", "C": "130°", "D": "140°"}, "correct_answer": "D"},
    {"id": 29, "difficulty": "medium", "question": "In trapezium ABCD with AB || DC, if ∠A = 75°, find corresponding angle at D.", "options": {"A": "75°", "B": "105°", "C": "15°", "D": "285°"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one corresponding angle is 30° more than half of other, find the angles.", "options": {"A": "60°, 60°", "B": "80°, 80°", "C": "100°, 100°", "D": "120°, 120°"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "If LM || NO and transversal PQ makes angle 48° with LM, what angle does it make with NO at corresponding position?", "options": {"A": "48°", "B": "132°", "C": "42°", "D": "138°"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "In rectangle ABCD, AB || DC. If ∠ABD = 55°, find corresponding angle at C.", "options": {"A": "55°", "B": "125°", "C": "35°", "D": "145°"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Two lines cut by transversal. Corresponding angles in ratio 5:7. If lines parallel, find angles.", "options": {"A": "75°, 105°", "B": "65°, 91°", "C": "70°, 98°", "D": "80°, 112°"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "If transversal cuts two parallel lines, and one corresponding angle is 40° less than three times the other, find both.", "options": {"A": "55°, 55°", "B": "60°, 60°", "C": "65°, 65°", "D": "70°, 70°"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "In figure, m || n and p is transversal. If ∠2 = 125°, find corresponding angle to ∠2.", "options": {"A": "55°", "B": "125°", "C": "35°", "D": "155°"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one corresponding angle measures (x² - 4)° and other (4x + 16)°, find x.", "options": {"A": "4", "B": "6", "C": "8", "D": "10"}, "correct_answer": "D"},
    {"id": 37, "difficulty": "medium", "question": "If lines parallel and corresponding angles differ by 50°, find the angles.", "options": {"A": "65°, 115°", "B": "70°, 120°", "C": "75°, 125°", "D": "80°, 130°"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "In triangle ABC, DE || BC with D on AB, E on AC. If ∠ADE = 55°, find corresponding angle at C.", "options": {"A": "55°", "B": "125°", "C": "35°", "D": "145°"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Two lines cut by transversal. If corresponding angles are (7x - 15)° and (5x + 25)° and lines parallel, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "If a || b and c transversal, and one corresponding angle is 20° more than two-fifths of other, find both equal angles.", "options": {"A": "70°", "B": "80°", "C": "90°", "D": "100°"}, "correct_answer": "D"},
    {"id": 41, "difficulty": "medium", "question": "In figure, PQ || RS. If ∠PAB = 70° and ∠ABS = 110°, which angles are corresponding?", "options": {"A": "∠PAB and ∠ABC", "B": "∠PAB and ∠ABS", "C": "∠PAB and ∠RBA", "D": "∠PAB and ∠BAS"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one corresponding angle is (x + 35)° and other (3x - 25)°, find x.", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "If lines l and m parallel and transversal t makes ∠1 = 62° with l, what is corresponding angle on m?", "options": {"A": "62°", "B": "118°", "C": "28°", "D": "152°"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "In rhombus ABCD, AB || DC. If ∠BAC = 40°, find corresponding angle at C.", "options": {"A": "40°", "B": "50°", "C": "80°", "D": "140°"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Two lines cut by transversal. Corresponding angles equal and each is 25° more than one-fifth of 180°. Find angles.", "options": {"A": "55°", "B": "60°", "C": "65°", "D": "70°"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "If a || b, and transversal c makes angles (4x + 15)° and (7x - 30)° as corresponding angles, find x.", "options": {"A": "12", "B": "15", "C": "18", "D": "21"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "In figure, AB || CD and EF is transversal. If ∠BEF = 105°, find corresponding angle to ∠BEF.", "options": {"A": "75°", "B": "105°", "C": "15°", "D": "165°"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "Two parallel lines cut by transversal. Corresponding angles in ratio 8:9. Find each angle.", "options": {"A": "80°, 90°", "B": "85°, 95°", "C": "84°, 96°", "D": "88°, 99°"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "If lines parallel and one corresponding angle is 15° more than 1.25 times other, find both.", "options": {"A": "60°, 60°", "B": "70°, 70°", "C": "80°, 80°", "D": "90°, 90°"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "In triangle ABC, DE || BC. If ∠ADE = (3x - 15)°, ∠ABC = (4x + 5)°, find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Two lines cut by transversal. If corresponding angles are (5x - 20)° and (3x + 40)° and lines parallel, find each.", "options": {"A": "80°", "B": "90°", "C": "100°", "D": "110°"}, "correct_answer": "D"},
    {"id": 52, "difficulty": "medium", "question": "If l || m, and transversal t makes ∠1 = (6x + 25)° with l and ∠2 = (8x - 15)° with m as corresponding angles, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "In parallelogram ABCD, AB || DC. If ∠DAB = 70°, find corresponding angle at C.", "options": {"A": "70°", "B": "110°", "C": "20°", "D": "160°"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one corresponding angle is 35° more than half the other, find both equal angles.", "options": {"A": "70°", "B": "80°", "C": "90°", "D": "100°"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "If a || b and c transversal, and corresponding angles are (x² + 5)° and (5x + 25)°, find x.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "In figure, PQ || RS. If ∠QPT = 45° and ∠TSR = 135°, find corresponding angle to ∠QPT.", "options": {"A": "45°", "B": "135°", "C": "55°", "D": "125°"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Two lines cut by transversal. Corresponding angles measure (4x + 25)° and (6x - 35)°. If lines parallel, find x.", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "medium", "question": "If lines parallel and corresponding angles are supplementary, what is each?", "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 = 85°, find corresponding angle at D.", "options": {"A": "85°", "B": "95°", "C": "5°", "D": "175°"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one corresponding angle is (3x + 55)° and other (5x + 15)°, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "If LM || NO, and transversal PQ makes ∠LMP = 58°, find corresponding angle on NO.", "options": {"A": "58°", "B": "122°", "C": "32°", "D": "148°"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "In rectangle PQRS, PQ || SR. If ∠PQS = 60°, find corresponding angle at R.", "options": {"A": "60°", "B": "120°", "C": "30°", "D": "150°"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Two lines cut by transversal. Corresponding angles in ratio 6:7. If lines parallel, find each.", "options": {"A": "72°, 84°", "B": "78°, 91°", "C": "84°, 98°", "D": "90°, 105°"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "If transversal cuts parallel lines, and one corresponding angle is 50° less than four times the other, find both.", "options": {"A": "46°, 46°", "B": "50°, 50°", "C": "54°, 54°", "D": "58°, 58°"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "In figure, a || b and c transversal. If ∠1 = 140°, find corresponding angle to ∠1.", "options": {"A": "40°", "B": "140°", "C": "50°", "D": "130°"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one corresponding angle measures (x² - 9)° and other (3x + 21)°, find x.", "options": {"A": "5", "B": "6", "C": "8", "D": "10"}, "correct_answer": "D"},
    {"id": 67, "difficulty": "medium", "question": "If lines parallel and corresponding angles differ by 60°, find the angles.", "options": {"A": "60°, 120°", "B": "65°, 125°", "C": "70°, 130°", "D": "75°, 135°"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "In triangle ABC, DE || BC. If ∠ADE = 70°, find corresponding angle at C.", "options": {"A": "70°", "B": "110°", "C": "20°", "D": "160°"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Two lines cut by transversal. If corresponding angles are (8x - 20)° and (6x + 40)° and lines parallel, find x.", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "If a || b and c transversal, and one corresponding angle is 30° more than three-sevenths of other, find both equal angles.", "options": {"A": "70°", "B": "80°", "C": "90°", "D": "105°"}, "correct_answer": "D"},
    {"id": 71, "difficulty": "medium", "question": "In figure, AB || CD. If ∠APQ = 130° and ∠PQD = 50°, which angles are corresponding?", "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 cut by transversal. If one corresponding angle is (x + 45)° and other (4x - 30)°, find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "If lines l and m parallel and transversal t makes ∠1 = 54° with l, what is corresponding angle on m?", "options": {"A": "54°", "B": "126°", "C": "36°", "D": "144°"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "In rhombus PQRS, PQ || SR. If ∠QPR = 35°, find corresponding angle at S.", "options": {"A": "35°", "B": "55°", "C": "70°", "D": "145°"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Two lines cut by transversal. Corresponding angles equal and each is 30° more than one-sixth of 180°. Find angles.", "options": {"A": "60°", "B": "65°", "C": "70°", "D": "75°"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "If a || b, and transversal c makes angles (5x + 20)° and (8x - 40)° as corresponding angles, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "In figure, PQ || RS and TU transversal. If ∠QTU = 85°, find corresponding angle to ∠QTU.", "options": {"A": "85°", "B": "95°", "C": "5°", "D": "175°"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Two parallel lines cut by transversal. Corresponding angles in ratio 9:10. Find each.", "options": {"A": "81°, 90°", "B": "85°, 95°", "C": "90°, 100°", "D": "95°, 105°"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "If lines parallel and one corresponding angle is 25° more than 1.5 times other, find both.", "options": {"A": "50°, 50°", "B": "60°, 60°", "C": "70°, 70°", "D": "80°, 80°"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "In triangle XYZ, ST || YZ. If ∠XST = (5x - 25)°, ∠XYZ = (4x + 15)°, find x.", "options": {"A": "30", "B": "35", "C": "40", "D": "45"}, "correct_answer": "C"},
    
    {"id": 81, "difficulty": "hard", "question": "In parallelogram ABCD, AB || DC and AD || BC. If ∠A = (4x + 15)° and ∠C = (6x - 35)°, find x using corresponding angles.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "Two parallel lines cut by transversal. If one corresponding angle is 25° less than four times its complement, find the angle.", "options": {"A": "55°", "B": "65°", "C": "75°", "D": "85°"}, "correct_answer": "C"},
    {"id": 83, "difficulty": "hard", "question": "In triangle ABC, DE || BC. If ∠ADE = (x² - 5)° and ∠ABC = (x² + 3x - 10)°, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 84, "difficulty": "hard", "question": "If lines parallel, and transversal p makes angles (x² + 3x)° and (2x² - 4x)° as corresponding angles, find all possible x.", "options": {"A": "0, 7", "B": "0, 8", "C": "0, 9", "D": "0, 10"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "In trapezium ABCD with AB || DC, if ∠A = (5x - 25)° and ∠D = (7x - 85)°, find x using corresponding angles.", "options": {"A": "30", "B": "40", "C": "50", "D": "60"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Two lines cut by transversal. If corresponding angles are (x³ - 8)° and (x² + 2x + 4)° and lines parallel, find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "In figure, AB || CD || EF, and transversal GH. If ∠1 = 70° and ∠2 = 110°, find all corresponding 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 cut by two transversals making corresponding angles (3x + 25)°, (4x - 15)°, and (2x + 35)° respectively, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "In parallelogram PQRS, PQ || SR and PS || QR. If ∠P = (6x - 20)°, ∠R = (4x + 40)°, find x using corresponding angles in two ways.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "Two lines cut by transversal. If corresponding angles satisfy 3∠A + 2∠B = 540° and lines parallel, find ∠A and ∠B.", "options": {"A": "108°, 108°", "B": "120°, 120°", "C": "90°, 135°", "D": "100°, 120°"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "In triangle ABC, DE || BC. If ∠ADE = (x² + 5)°, ∠ABC = (3x + 25)°, find all possible x.", "options": {"A": "4, 5", "B": "5, 6", "C": "6, 7", "D": "7, 8"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "If lines parallel and corresponding angles are such that one angle's measure is geometric mean of 25° and 100°, find both.", "options": {"A": "50°, 50°", "B": "60°, 60°", "C": "70°, 70°", "D": "80°, 80°"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "In figure, AB || CD and EF || GH. If ∠1 = 80° and ∠2 = 100°, find all corresponding angles and measures.", "options": {"A": "∠1 = ∠3 = 80°, ∠2 = ∠4 = 100°", "B": "∠1 = ∠4 = 80°, ∠2 = ∠3 = 100°", "C": "∠1 = ∠2 = 80°, ∠3 = ∠4 = 100°", "D": "∠1 = 80°, ∠2 = 100°, ∠3 = 80°, ∠4 = 80°"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Two parallel lines cut by transversal. Corresponding angles in ratio (√3 + 1):(√3 - 1). Find angles.", "options": {"A": "75°, 15°", "B": "105°, 75°", "C": "120°, 60°", "D": "135°, 45°"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "In complex figure with multiple parallel lines and transversals, if ∠1 = 35°, ∠2 = 145°, ∠3 = 35°, ∠4 = 145°, identify all corresponding angle pairs.", "options": {"A": "∠1 & ∠3, ∠2 & ∠4", "B": "∠1 & ∠4, ∠2 & ∠3", "C": "∠1 & ∠2, ∠3 & ∠4", "D": "All are corresponding"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "If lines parallel and transversal makes angles forming arithmetic progression with sum 360°, find all corresponding angles.", "options": {"A": "60°, 80°, 100°, 120°", "B": "70°, 90°, 110°, 90°", "C": "80°, 100°, 80°, 100°", "D": "90°, 90°, 90°, 90°"}, "correct_answer": "D"},
    {"id": 97, "difficulty": "hard", "question": "In quadrilateral ABCD with AB || DC and AD || BC, if ∠A = (3x² - 10x)° and ∠C = (x² + 20x)°, find x.", "options": {"A": "0, 15", "B": "0, 20", "C": "0, 25", "D": "0, 30"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "Two lines cut by transversal. If corresponding angles satisfy sin(∠A) = sin(∠B) and lines parallel, find ∠A and ∠B.", "options": {"A": "45°, 135°", "B": "60°, 120°", "C": "30°, 150°", "D": "∠A = ∠B"}, "correct_answer": "D"},
    {"id": 99, "difficulty": "hard", "question": "In figure with three parallel lines cut by two transversals, if ∠1 = (4x + 30)°, ∠2 = (6x - 40)°, ∠3 = (5x - 20)°, and all corresponding angles equal, find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "D"},
    {"id": 100, "difficulty": "hard", "question": "If corresponding angles are such that their measures in degrees are consecutive even integers whose sum is 204, find the angles.", "options": {"A": "100°, 100°, 102°, 102°", "B": "100°, 104°, 100°, 104°", "C": "102°, 102°, 102°, 102°", "D": "98°, 106°, 98°, 106°"}, "correct_answer": "B"}
  ]
}