{
  "title": "Parallel Lines and Transversal - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "A line cutting two or more lines is called:", "options": {"A": "Parallel line", "B": "Transversal", "C": "Perpendicular", "D": "Intersecting line"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "If two parallel lines are cut by transversal, alternate interior angles are:", "options": {"A": "Supplementary", "B": "Complementary", "C": "Equal", "D": "Right angles"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "Corresponding angles are equal when lines are:", "options": {"A": "Intersecting", "B": "Parallel", "C": "Perpendicular", "D": "Coincident"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "If lines are parallel, same-side interior angles are:", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "How many angles are formed when transversal cuts two lines?", "options": {"A": "4", "B": "6", "C": "8", "D": "10"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "If ∠1 and ∠2 are corresponding angles and lines are parallel, then:", "options": {"A": "∠1 = ∠2", "B": "∠1 + ∠2 = 90°", "C": "∠1 + ∠2 = 180°", "D": "∠1 = 180° - ∠2"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Alternate exterior angles are equal when lines are:", "options": {"A": "Intersecting", "B": "Parallel", "C": "Perpendicular", "D": "Skew"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "If l || m and transversal t, which angles are equal?", "options": {"A": "Corresponding angles", "B": "Adjacent angles", "C": "Linear pair", "D": "Vertical angles"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "If two lines are parallel, interior angles on same side of transversal sum to:", "options": {"A": "90°", "B": "180°", "C": "270°", "D": "360°"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Which is NOT formed by transversal cutting parallel lines?", "options": {"A": "Alternate interior angles", "B": "Vertical angles", "C": "Corresponding angles", "D": "Same-side interior angles"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "If lines are not parallel, corresponding angles are:", "options": {"A": "Always equal", "B": "Never equal", "C": "Sometimes equal", "D": "Always supplementary"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "To prove lines parallel, we can show:", "options": {"A": "Corresponding angles are equal", "B": "Vertical angles are equal", "C": "Adjacent angles are equal", "D": "Linear pair sums to 180°"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "If a transversal is perpendicular to one parallel line, it is:", "options": {"A": "Parallel to other", "B": "Perpendicular to other", "C": "Intersecting to other", "D": "Skew to other"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "If ∠3 = 60° and lines are parallel, its corresponding angle is:", "options": {"A": "30°", "B": "60°", "C": "120°", "D": "180°"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "Same-side exterior angles are supplementary when lines are:", "options": {"A": "Intersecting", "B": "Parallel", "C": "Perpendicular", "D": "Coincident"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "If two lines are cut by transversal and alternate interior angles are equal, lines are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting", "D": "Coincident"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "How many pairs of corresponding angles?", "options": {"A": "2", "B": "3", "C": "4", "D": "6"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "If lines parallel, each pair of alternate exterior angles are:", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Transversal creates how many angle pairs?", "options": {"A": "4 types of pairs", "B": "5 types of pairs", "C": "6 types of pairs", "D": "8 types of pairs"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "If lines parallel and one angle is 45°, its alternate interior angle is:", "options": {"A": "45°", "B": "135°", "C": "90°", "D": "180°"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "If l || m and transversal t makes ∠1 = 70°, find ∠3 (alternate interior).", "options": {"A": "70°", "B": "110°", "C": "20°", "D": "160°"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "In figure, AB || CD. If ∠APQ = 50°, find ∠PQD (same-side interior).", "options": {"A": "50°", "B": "130°", "C": "40°", "D": "140°"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "If parallel lines cut by transversal and one interior angle is (3x + 20)°, its same-side interior is (5x - 40)°. Find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "In parallelogram ABCD, AB || DC. If ∠A = 65°, find ∠C using parallel lines properties.", "options": {"A": "65°", "B": "115°", "C": "25°", "D": "295°"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "If l || m and transversal, corresponding angles are (4x + 10)° and (6x - 20)°. Find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one alternate interior angle is 20° more than half of other, find both.", "options": {"A": "60°, 60°", "B": "70°, 70°", "C": "80°, 80°", "D": "90°, 90°"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "In figure, a || b. If ∠1 = 120°, find ∠6 (alternate exterior).", "options": {"A": "60°", "B": "120°", "C": "30°", "D": "150°"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "If lines parallel and same-side interior angles are (7x - 10)° and (5x + 30)°, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "In trapezium ABCD with AB || DC, if ∠A = 80°, find ∠D (same-side interior).", "options": {"A": "80°", "B": "100°", "C": "10°", "D": "170°"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one corresponding angle is 30° more than 2/3 of other, find both.", "options": {"A": "72°, 72°", "B": "75°, 75°", "C": "78°, 78°", "D": "81°, 81°"}, "correct_answer": "D"},
    {"id": 31, "difficulty": "medium", "question": "If LM || NO and transversal PQ makes ∠LMP = 55°, find ∠MNO (corresponding).", "options": {"A": "55°", "B": "125°", "C": "35°", "D": "145°"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "In rectangle ABCD, AB || DC. If ∠ABD = 60°, find ∠BDC (alternate interior).", "options": {"A": "60°", "B": "120°", "C": "30°", "D": "150°"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Two parallel lines cut by transversal. Alternate interior angles in ratio 5:7. Find each.", "options": {"A": "75°, 105°", "B": "65°, 91°", "C": "70°, 98°", "D": "80°, 112°"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "If transversal cuts parallel lines, and one same-side exterior is 50° less than three times other, find both.", "options": {"A": "57.5°, 122.5°", "B": "60°, 120°", "C": "62.5°, 117.5°", "D": "65°, 115°"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "In figure, m || n. If ∠2 = 135°, find ∠7 (corresponding).", "options": {"A": "45°", "B": "135°", "C": "35°", "D": "155°"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one alternate exterior measures (x² - 9)° and other (4x + 3)°, find x.", "options": {"A": "4", "B": "6", "C": "8", "D": "10"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "If lines parallel and same-side interior angles differ by 60°, find them.", "options": {"A": "60°, 120°", "B": "70°, 130°", "C": "80°, 140°", "D": "90°, 150°"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "In triangle ABC, DE || BC. If ∠ADE = 65°, find ∠ABC (corresponding).", "options": {"A": "65°", "B": "115°", "C": "25°", "D": "295°"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If alternate interior are (8x - 20)° and (6x + 40)°, find x.", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "If lines parallel and one corresponding angle is 25° more than 3/5 of other, find both.", "options": {"A": "62.5°, 62.5°", "B": "65°, 65°", "C": "67.5°, 67.5°", "D": "70°, 70°"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "In figure, PQ || RS. If ∠PAB = 75°, find ∠ABS (same-side interior).", "options": {"A": "75°", "B": "105°", "C": "15°", "D": "165°"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one corresponding angle is (x + 40)° and other (3x - 20)°, find x.", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "If lines parallel and transversal makes ∠1 = 58° with one line, corresponding angle on other line is:", "options": {"A": "58°", "B": "122°", "C": "32°", "D": "148°"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "In rhombus ABCD, AB || DC. If ∠BAC = 35°, find ∠ACD (alternate interior).", "options": {"A": "35°", "B": "55°", "C": "70°", "D": "145°"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Two parallel lines cut by transversal. Same-side interior angles equal and each is 25° more than one-fourth of 180°. Find angles.", "options": {"A": "60°", "B": "65°", "C": "70°", "D": "75°"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "If lines parallel, and transversal makes angles (5x + 15)° and (8x - 45)° as alternate exterior, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "In figure, AB || CD. If ∠BEF = 115°, find ∠DFE (same-side interior).", "options": {"A": "65°", "B": "115°", "C": "25°", "D": "155°"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Two parallel lines cut by transversal. Corresponding angles in ratio 8:9. Find each.", "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 alternate interior angle is 20° more than 1.25 times other, find both.", "options": {"A": "80°, 80°", "B": "85°, 85°", "C": "90°, 90°", "D": "95°, 95°"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "In triangle ABC, DE || BC. If ∠ADE = (4x - 20)°, ∠ABC = (3x + 25)°, find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If alternate exterior are (6x - 25)° and (4x + 35)°, find x.", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "If lines parallel, and transversal makes ∠1 = (7x + 25)° with one line and ∠2 = (9x - 15)° with other as corresponding, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "In parallelogram ABCD, AB || DC. If ∠DAB = 75°, find ∠BCD (corresponding).", "options": {"A": "75°", "B": "105°", "C": "15°", "D": "295°"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one same-side interior is 40° more than half the other, find both (supplementary).", "options": {"A": "66.67°, 113.33°", "B": "70°, 110°", "C": "75°, 105°", "D": "80°, 100°"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "If lines parallel and transversal, and alternate interior are (x² + 10)° and (5x + 10)°, find x.", "options": {"A": "0, 5", "B": "5, 10", "C": "10, 15", "D": "15, 20"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "In figure, PQ || RS. If ∠QPT = 50°, find ∠TSR (corresponding).", "options": {"A": "50°", "B": "130°", "C": "40°", "D": "140°"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Two parallel lines cut by transversal. Same-side exterior angles measure (5x + 25)° and (7x - 35)°. Find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "A"},
    {"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 ∠D (same-side interior).", "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 alternate interior is (4x + 55)° and other (6x + 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 = 62°, find ∠MNO (corresponding).", "options": {"A": "62°", "B": "118°", "C": "28°", "D": "152°"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "In rectangle PQRS, PQ || SR. If ∠PQS = 65°, find ∠QSR (alternate interior).", "options": {"A": "65°", "B": "115°", "C": "25°", "D": "145°"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Two parallel lines cut by transversal. Alternate exterior angles in ratio 6:7. 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 60° less than four times the other, find both.", "options": {"A": "48°, 48°", "B": "50°, 50°", "C": "52°, 52°", "D": "54°, 54°"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "In figure, a || b. If ∠1 = 140°, find ∠5 (alternate exterior).", "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 same-side interior measures (x² - 16)° and other (3x + 44)°, find x.", "options": {"A": "5", "B": "6", "C": "10", "D": "12"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "If lines parallel and alternate exterior angles differ by 80°, find them.", "options": {"A": "50°, 130°", "B": "55°, 135°", "C": "60°, 140°", "D": "65°, 145°"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "In triangle ABC, DE || BC. If ∠ADE = 75°, find ∠ABC (corresponding).", "options": {"A": "75°", "B": "105°", "C": "15°", "D": "295°"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If corresponding angles are (9x - 30)° and (7x + 50)°, find x.", "options": {"A": "35", "B": "40", "C": "45", "D": "50"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "If lines parallel and one same-side exterior is 35° more than 2/7 of other, find both (supplementary).", "options": {"A": "95°, 85°", "B": "100°, 80°", "C": "105°, 75°", "D": "110°, 70°"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "In figure, AB || CD. If ∠APQ = 135°, find ∠PQD (same-side interior).", "options": {"A": "45°", "B": "135°", "C": "55°", "D": "125°"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Two parallel lines cut by transversal. If one alternate interior is (x + 50)° and other (4x - 10)°, find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "If lines parallel and transversal makes ∠1 = 54° with one line, alternate interior on other line is:", "options": {"A": "54°", "B": "126°", "C": "36°", "D": "144°"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "In rhombus PQRS, PQ || SR. If ∠QPR = 40°, find ∠PRS (alternate interior).", "options": {"A": "40°", "B": "50°", "C": "80°", "D": "140°"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Two parallel lines cut by transversal. Same-side exterior angles equal and each is 30° more than one-fifth of 180°. Find angles.", "options": {"A": "60°", "B": "65°", "C": "70°", "D": "75°"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "If lines parallel, and transversal makes angles (6x + 25)° and (10x - 55)° as corresponding, 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 = 95°, find ∠TUR (same-side interior).", "options": {"A": "85°", "B": "95°", "C": "5°", "D": "175°"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Two parallel lines cut by transversal. Alternate interior 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 30° more than 1.4 times other, find both.", "options": {"A": "70°, 70°", "B": "75°, 75°", "C": "80°, 80°", "D": "85°, 85°"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "In triangle XYZ, ST || YZ. If ∠XST = (6x - 35)°, ∠XYZ = (5x + 20)°, find x.", "options": {"A": "40", "B": "45", "C": "50", "D": "55"}, "correct_answer": "D"},
    
    {"id": 81, "difficulty": "hard", "question": "In parallelogram ABCD, AB || DC and AD || BC. If ∠A = (5x + 15)° and ∠C = (7x - 35)°, find x using parallel lines properties.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "Three parallel lines cut by two transversals. If corresponding angles are (3x + 25)°, (4x - 15)°, (2x + 35)°, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"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 + 4x)° and (2x² - 2x)° as alternate interior, find all possible x.", "options": {"A": "0, 6", "B": "0, 7", "C": "0, 8", "D": "0, 9"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "In trapezium ABCD with AB || DC, if ∠A = (6x - 30)° and ∠D = (8x - 90)°, find x using parallel lines properties.", "options": {"A": "30", "B": "40", "C": "50", "D": "60"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Two parallel lines cut by transversal. If alternate interior angles are (x³ - 8)° and (x² + 2x + 4)°, find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "In figure, AB || CD || EF. If ∠1 = 75°, ∠2 = 105°, find all angle 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 transversals making angles in arithmetic progression with sum 540°, find middle angle.", "options": {"A": "90°", "B": "120°", "C": "150°", "D": "180°"}, "correct_answer": "D"},
    {"id": 89, "difficulty": "hard", "question": "In parallelogram PQRS, PQ || SR and PS || QR. If ∠P = (7x - 25)°, ∠R = (5x + 35)°, find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "Two parallel lines cut by transversal. If corresponding angles satisfy 4∠A + 3∠B = 720°, find ∠A and ∠B.", "options": {"A": "120°, 120°", "B": "130°, 130°", "C": "140°, 140°", "D": "150°, 150°"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "In triangle ABC, DE || BC. If ∠ADE = (x² + 10)°, ∠ABC = (4x + 25)°, find all possible x.", "options": {"A": "3, 5", "B": "4, 5", "C": "5, 7", "D": "6, 8"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "If lines parallel and corresponding angles are such that one is harmonic mean of 40° and 120°, find both.", "options": {"A": "60°, 60°", "B": "70°, 70°", "C": "80°, 80°", "D": "90°, 90°"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "In figure, AB || CD and EF || GH. If ∠1 = 85°, ∠2 = 95°, find all angles.", "options": {"A": "∠1 = ∠3 = 85°, ∠2 = ∠4 = 95°", "B": "∠1 = ∠4 = 85°, ∠2 = ∠3 = 95°", "C": "∠1 = ∠2 = 85°, ∠3 = ∠4 = 95°", "D": "∠1 = 85°, ∠2 = 95°, ∠3 = 85°, ∠4 = 85°"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Two parallel lines cut by transversal. Alternate interior angles in ratio (√3 + 1):(√3 - 1). Find angles.", "options": {"A": "75°, 105°", "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 = 30°, ∠2 = 150°, ∠3 = 30°, ∠4 = 150°, identify all angle pairs.", "options": {"A": "∠1 & ∠3 alt int, ∠2 & ∠4 alt int", "B": "∠1 & ∠4 corr, ∠2 & ∠3 corr", "C": "∠1 & ∠2 same-side int, ∠3 & ∠4 same-side int", "D": "All are corresponding"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "If lines parallel and transversal makes angles forming arithmetic progression with common difference 15°, find all eight angles.", "options": {"A": "30°, 45°, 60°, 75°, 150°, 135°, 120°, 105°", "B": "35°, 50°, 65°, 80°, 145°, 130°, 115°, 100°", "C": "40°, 55°, 70°, 85°, 140°, 125°, 110°, 95°", "D": "45°, 60°, 75°, 90°, 135°, 120°, 105°, 90°"}, "correct_answer": "D"},
    {"id": 97, "difficulty": "hard", "question": "In quadrilateral ABCD with AB || DC and AD || BC, if ∠A = (4x² - 20x)° and ∠C = (x² + 25x)°, find x.", "options": {"A": "0, 15", "B": "0, 20", "C": "0, 25", "D": "0, 30"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "Two parallel lines cut by transversal. If alternate exterior angles satisfy sin(∠A) = sin(∠B), find all possibilities.", "options": {"A": "∠A = ∠B or ∠A + ∠B = 180°", "B": "∠A = ∠B only", "C": "∠A + ∠B = 90° only", "D": "∠A = 180° - ∠B only"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "In figure with three parallel lines cut by two transversals, if ∠1 = (5x + 40)°, ∠2 = (7x - 50)°, ∠3 = (6x - 30)°, and all corresponding angles equal, find x.", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "If corresponding angles are consecutive multiples of 15°, find all eight angles.", "options": {"A": "15°, 30°, 45°, 60°, 165°, 150°, 135°, 120°", "B": "20°, 40°, 60°, 80°, 160°, 140°, 120°, 100°", "C": "25°, 50°, 75°, 100°, 155°, 130°, 105°, 80°", "D": "30°, 60°, 90°, 120°, 150°, 120°, 90°, 60°"}, "correct_answer": "D"}
  ]
}