{
  "title": "Intersecting Lines - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "When two lines intersect, they form:", "options": {"A": "Two angles", "B": "Four angles", "C": "Six angles", "D": "Eight angles"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "Vertically opposite angles are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Equal", "D": "Adjacent"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "If two lines intersect at 90°, they are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Collinear", "D": "Concurrent"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Sum of all angles around a point is:", "options": {"A": "90°", "B": "180°", "C": "270°", "D": "360°"}, "correct_answer": "D"},
    {"id": 5, "difficulty": "easy", "question": "If two lines intersect, vertically opposite angles are always:", "options": {"A": "Acute", "B": "Equal", "C": "Supplementary", "D": "Complementary"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Adjacent angles formed by intersecting lines are:", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "If two lines intersect and one angle is 40°, its vertically opposite angle is:", "options": {"A": "40°", "B": "50°", "C": "140°", "D": "180°"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Maximum number of intersection points of two lines is:", "options": {"A": "0", "B": "1", "C": "2", "D": "Infinite"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "If two lines intersect forming 60° angle, adjacent angle is:", "options": {"A": "30°", "B": "60°", "C": "120°", "D": "180°"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "Two lines intersect. If one angle is 90°, all other angles are:", "options": {"A": "45°", "B": "90°", "C": "180°", "D": "360°"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Sum of adjacent angles formed by intersecting lines is:", "options": {"A": "90°", "B": "180°", "C": "270°", "D": "360°"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "If three lines intersect at one point, they are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Concurrent", "D": "Collinear"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "When two lines intersect, sum of all four angles is:", "options": {"A": "180°", "B": "270°", "C": "360°", "D": "540°"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "If two lines intersect forming angles 30°, 150°, 30°, 150°, they are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Intersecting but not perpendicular", "D": "Coincident"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "Vertical angles theorem states:", "options": {"A": "Vertical angles are supplementary", "B": "Vertical angles are complementary", "C": "Vertical angles are equal", "D": "Vertical angles are right angles"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "If two lines are perpendicular, each angle formed is:", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "Two lines intersect. If one angle is x°, its vertically opposite is:", "options": {"A": "(90-x)°", "B": "(180-x)°", "C": "x°", "D": "(360-x)°"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "Adjacent angles on straight line are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Equal", "D": "Vertical"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "If two lines intersect at point O, angles around O sum to:", "options": {"A": "180°", "B": "270°", "C": "360°", "D": "540°"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Lines that cross each other are called:", "options": {"A": "Parallel", "B": "Intersecting", "C": "Perpendicular", "D": "Skew"}, "correct_answer": "B"},
    
    {"id": 21, "difficulty": "medium", "question": "Two lines intersect. If one angle is 75°, find all other angles.", "options": {"A": "75°, 105°, 105°", "B": "75°, 75°, 105°", "C": "75°, 105°, 75°", "D": "105°, 105°, 105°"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "If two lines intersect forming angles (2x + 10)° and (3x - 20)°, find x.", "options": {"A": "30", "B": "35", "C": "38", "D": "42"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "Two lines intersect. Vertically opposite angles are in ratio 3:5. Find all angles.", "options": {"A": "67.5°, 112.5°, 67.5°, 112.5°", "B": "60°, 120°, 60°, 120°", "C": "75°, 105°, 75°, 105°", "D": "80°, 100°, 80°, 100°"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "If two lines intersect and one angle is 25° more than its adjacent angle, find all angles.", "options": {"A": "77.5°, 102.5°, 77.5°, 102.5°", "B": "75°, 105°, 75°, 105°", "C": "80°, 100°, 80°, 100°", "D": "85°, 95°, 85°, 95°"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Three lines intersect at one point making angles 40°, 80°, and x°. Find x.", "options": {"A": "60°", "B": "120°", "C": "180°", "D": "240°"}, "correct_answer": "D"},
    {"id": 26, "difficulty": "medium", "question": "If two lines intersect forming angles (4x - 15)° and (3x + 25)°, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "Two lines intersect. If difference between two adjacent angles is 30°, find all angles.", "options": {"A": "75°, 105°, 75°, 105°", "B": "70°, 110°, 70°, 110°", "C": "80°, 100°, 80°, 100°", "D": "85°, 95°, 85°, 95°"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "If two lines intersect at right angles, each angle formed is:", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "Two lines intersect. If sum of two adjacent angles is 210°, find all angles.", "options": {"A": "105°, 105°, 75°, 75°", "B": "105°, 75°, 105°, 75°", "C": "110°, 70°, 110°, 70°", "D": "115°, 65°, 115°, 65°"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "If three lines intersect pairwise, maximum intersection points:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "Two lines intersect. If one angle is (5x - 20)° and its vertically opposite is (3x + 40)°, find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "If two lines intersect forming angles in ratio 2:3, find all angles.", "options": {"A": "72°, 108°, 72°, 108°", "B": "60°, 120°, 60°, 120°", "C": "80°, 100°, 80°, 100°", "D": "90°, 90°, 90°, 90°"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Two lines intersect. If one angle is twice its adjacent, find all angles.", "options": {"A": "60°, 120°, 60°, 120°", "B": "50°, 130°, 50°, 130°", "C": "70°, 110°, 70°, 110°", "D": "80°, 100°, 80°, 100°"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "If two lines intersect and (x + 20)° and (2x - 40)° are vertically opposite, find x.", "options": {"A": "40", "B": "50", "C": "60", "D": "70"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "Three lines concurrent. If angles are 2x°, 3x°, and 5x°, find x.", "options": {"A": "18", "B": "20", "C": "24", "D": "36"}, "correct_answer": "D"},
    {"id": 36, "difficulty": "medium", "question": "Two lines intersect. If one angle is 15° less than three times its adjacent, find all angles.", "options": {"A": "48.75°, 131.25°, 48.75°, 131.25°", "B": "50°, 130°, 50°, 130°", "C": "55°, 125°, 55°, 125°", "D": "60°, 120°, 60°, 120°"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "medium", "question": "If two lines intersect forming angles (6x - 25)° and (4x + 15)°, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Two lines intersect. Sum of two vertically opposite angles is 240°. Find all angles.", "options": {"A": "120°, 60°, 120°, 60°", "B": "110°, 70°, 110°, 70°", "C": "100°, 80°, 100°, 80°", "D": "90°, 90°, 90°, 90°"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "If two lines are perpendicular, adjacent angles are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Equal", "D": "Right angles"}, "correct_answer": "D"},
    {"id": 40, "difficulty": "medium", "question": "Two lines intersect. If one angle is (x² - 10)° and vertically opposite is (3x + 20)°, find x.", "options": {"A": "5", "B": "6", "C": "10", "D": "15"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "If two lines intersect forming angles in ratio 5:7, find smaller angle.", "options": {"A": "60°", "B": "65°", "C": "70°", "D": "75°"}, "correct_answer": "D"},
    {"id": 42, "difficulty": "medium", "question": "Two lines intersect. Difference between two adjacent angles is 40°. Find larger.", "options": {"A": "100°", "B": "110°", "C": "120°", "D": "130°"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "If (3x + 10)° and (5x - 30)° are vertically opposite, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "Three concurrent lines. Angles are x°, 2x°, and 3x°. Find x.", "options": {"A": "30", "B": "45", "C": "60", "D": "90"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "Two lines intersect. If one angle is 20° more than half its adjacent, find all angles.", "options": {"A": "73.33°, 106.67°, 73.33°, 106.67°", "B": "75°, 105°, 75°, 105°", "C": "80°, 100°, 80°, 100°", "D": "85°, 95°, 85°, 95°"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "If two lines intersect forming angles (7x - 15)° and (5x + 25)°, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Two lines intersect. Sum of three angles is 320°. Find fourth angle.", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "If two lines are perpendicular, all angles are:", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Straight"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "Two lines intersect. If (x² - 5)° and (4x + 15)° are vertically opposite, find x.", "options": {"A": "4", "B": "5", "C": "10", "D": "15"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "If two lines intersect forming angles in ratio 3:4, find all angles.", "options": {"A": "77.14°, 102.86°, 77.14°, 102.86°", "B": "75°, 105°, 75°, 105°", "C": "80°, 100°, 80°, 100°", "D": "85°, 95°, 85°, 95°"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Two lines intersect. Difference between vertically opposite angles is 0° because:", "options": {"A": "They're supplementary", "B": "They're equal", "C": "They're complementary", "D": "They're adjacent"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "If (4x - 20)° and (6x - 60)° are vertically opposite, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "Three lines concurrent. Angles are 40°, 2x°, and 3x°. Find x.", "options": {"A": "40", "B": "50", "C": "64", "D": "72"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "Two lines intersect. If one angle is 25° less than twice its adjacent, find all angles.", "options": {"A": "68.33°, 111.67°, 68.33°, 111.67°", "B": "70°, 110°, 70°, 110°", "C": "75°, 105°, 75°, 105°", "D": "80°, 100°, 80°, 100°"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "If two lines intersect forming angles (8x - 30)° and (6x + 10)°, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "Two lines intersect. Three angles sum to 280°. Find fourth.", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "When lines intersect at 90°, they form how many right angles?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "D"},
    {"id": 58, "difficulty": "medium", "question": "Two lines intersect. If (x² + 10)° and (5x + 10)° are vertically opposite, find x.", "options": {"A": "0, 5", "B": "0, 10", "C": "5, 10", "D": "10, 15"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "If two lines intersect forming angles in ratio 4:5, find smaller.", "options": {"A": "70°", "B": "75°", "C": "80°", "D": "85°"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "Two lines intersect. Difference between adjacent angles is 50°. Find smaller.", "options": {"A": "55°", "B": "60°", "C": "65°", "D": "70°"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "If (5x + 15)° and (7x - 35)° are vertically opposite, find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "Three concurrent lines. Angles are x°, x+20°, x+40°. Find x.", "options": {"A": "80", "B": "90", "C": "100", "D": "110"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "Two lines intersect. If one angle is 30° more than 2/3 of its adjacent, find all angles.", "options": {"A": "72°, 108°, 72°, 108°", "B": "75°, 105°, 75°, 105°", "C": "78°, 102°, 78°, 102°", "D": "80°, 100°, 80°, 100°"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "If two lines intersect forming angles (9x - 40)° and (7x + 20)°, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "D"},
    {"id": 65, "difficulty": "medium", "question": "Two lines intersect. Sum of two adjacent angles is 190°. Find all angles.", "options": {"A": "95°, 85°, 95°, 85°", "B": "100°, 80°, 100°, 80°", "C": "105°, 75°, 105°, 75°", "D": "110°, 70°, 110°, 70°"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Maximum intersection points of 4 lines in plane:", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "Two lines intersect. If (2x² - 5)° and (4x + 15)° are vertically opposite, find x.", "options": {"A": "2.5", "B": "5", "C": "7.5", "D": "10"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "If two lines intersect forming angles in ratio 5:6, find larger.", "options": {"A": "81.82°", "B": "85.45°", "C": "90°", "D": "98.18°"}, "correct_answer": "D"},
    {"id": 69, "difficulty": "medium", "question": "Two lines intersect. Difference between vertically opposite angles is:", "options": {"A": "Always 0°", "B": "Always 90°", "C": "Always 180°", "D": "Variable"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "If (6x - 25)° and (4x + 35)° are vertically opposite, find x.", "options": {"A": "25", "B": "30", "C": "35", "D": "40"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "Three concurrent lines. Angles are 2x°, 3x°, 7x°. Find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "D"},
    {"id": 72, "difficulty": "medium", "question": "Two lines intersect. If one angle is 40° more than 3/5 of its adjacent, find all angles.", "options": {"A": "75°, 105°, 75°, 105°", "B": "80°, 100°, 80°, 100°", "C": "85°, 95°, 85°, 95°", "D": "90°, 90°, 90°, 90°"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "If two lines intersect forming angles (10x - 50)° and (8x + 10)°, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "D"},
    {"id": 74, "difficulty": "medium", "question": "Two lines intersect. Three angles are 80°, 100°, 80°. Find fourth.", "options": {"A": "80°", "B": "90°", "C": "100°", "D": "110°"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "When two lines intersect, adjacent angles are always:", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "Two lines intersect. If (3x² - 20)° and (5x + 40)° are vertically opposite, find x.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "If two lines intersect forming angles in ratio 7:8, find smaller.", "options": {"A": "84°", "B": "96°", "C": "102°", "D": "108°"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Two lines intersect. Sum of two vertically opposite angles is 200°. Find each.", "options": {"A": "80°, 100°", "B": "90°, 110°", "C": "100°, 100°", "D": "110°, 90°"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "If (7x - 30)° and (5x + 50)° are vertically opposite, find x.", "options": {"A": "30", "B": "35", "C": "40", "D": "45"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "Three concurrent lines. Angles are x°, 2x°, 6x°. Find x.", "options": {"A": "20", "B": "30", "C": "40", "D": "50"}, "correct_answer": "C"},
    
    {"id": 81, "difficulty": "hard", "question": "Two lines intersect. If one angle is (3x + 20)° and its adjacent is (5x - 40)°, and vertically opposite to first is (2x + 80)°, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "Three lines intersect pairwise forming triangle. If angles at intersection points are 40°, 60°, 80°, find other angles in figure.", "options": {"A": "100°, 120°, 140°", "B": "110°, 130°, 150°", "C": "120°, 140°, 160°", "D": "130°, 150°, 170°"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "If two lines intersect and angles satisfy: ∠1 + ∠2 = 150°, ∠2 + ∠3 = 200°, find all angles.", "options": {"A": "50°, 100°, 50°, 160°", "B": "60°, 90°, 60°, 150°", "C": "70°, 80°, 70°, 140°", "D": "80°, 70°, 80°, 130°"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Four lines intersect at most how many points?", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "Two lines intersect. Angles are (x² - 5x)°, (x² + 5)°, (2x² - 10)°, and (3x + 15)°. Find x.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "If three lines are concurrent and angles are in arithmetic progression with sum 360°, find middle angle.", "options": {"A": "60°", "B": "90°", "C": "120°", "D": "150°"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "Two lines intersect. If ∠1 = 2∠2 = 3∠3, find ∠4.", "options": {"A": "30°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "D"},
    {"id": 88, "difficulty": "hard", "question": "Maximum intersection points of n lines in plane:", "options": {"A": "n", "B": "n(n-1)/2", "C": "n(n+1)/2", "D": "2n"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "If two lines intersect forming angles such that ∠1 - ∠2 = 40°, ∠2 + ∠3 = 180°, find all angles.", "options": {"A": "110°, 70°, 110°, 70°", "B": "100°, 60°, 100°, 100°", "C": "120°, 80°, 120°, 40°", "D": "130°, 90°, 130°, 10°"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Three lines intersect forming triangle. Sum of angles at vertices of triangle is 180°. If angles at intersections are 50°, 70°, x°, find x.", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "B"},
    {"id": 91, "difficulty": "hard", "question": "Two lines intersect. If angles are in ratio 1:2:3:4, find smallest.", "options": {"A": "30°", "B": "36°", "C": "40°", "D": "45°"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "If four lines are concurrent, sum of all angles around point:", "options": {"A": "180°", "B": "270°", "C": "360°", "D": "540°"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "Two lines intersect. Angles satisfy: ∠1 = ∠2 + ∠3, ∠4 = ∠2 - ∠3 + 90°. Find all angles.", "options": {"A": "120°, 60°, 60°, 120°", "B": "135°, 45°, 45°, 135°", "C": "150°, 30°, 30°, 150°", "D": "160°, 20°, 20°, 160°"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "Minimum intersection points of 5 lines (no two parallel, no three concurrent):", "options": {"A": "5", "B": "8", "C": "10", "D": "12"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "If two lines intersect and angles are (log₂x)°, (log₄x)°, (log₈x)°, (log₁₆x)°, find x.", "options": {"A": "16", "B": "32", "C": "64", "D": "128"}, "correct_answer": "C"},
    {"id": 96, "difficulty": "hard", "question": "Three lines intersect pairwise. If angles at one intersection are 70° and 110°, and at another are 80° and 100°, find angles at third intersection.", "options": {"A": "60° and 120°", "B": "65° and 115°", "C": "70° and 110°", "D": "75° and 105°"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Two lines intersect. If angles form arithmetic progression, find all possible angle sets.", "options": {"A": "45°, 135°, 45°, 135° only", "B": "60°, 120°, 60°, 120° only", "C": "a°, (180-a)°, a°, (180-a)° for any a", "D": "90°, 90°, 90°, 90° only"}, "correct_answer": "C"},
    {"id": 98, "difficulty": "hard", "question": "If n lines are concurrent, sum of angles around point:", "options": {"A": "90n°", "B": "180n°", "C": "360° regardless of n", "D": "720°"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "Two lines intersect. Angles satisfy: sin(∠1) = cos(∠2), and ∠1 + ∠3 = 180°. Find all angles.", "options": {"A": "45°, 135°, 45°, 135°", "B": "60°, 120°, 60°, 120°", "C": "30°, 150°, 30°, 150°", "D": "90°, 90°, 90°, 90°"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Maximum number of acute angles formed by two intersecting lines:", "options": {"A": "0", "B": "2", "C": "4", "D": "6"}, "correct_answer": "B"}
  ]
}