{
  "title": "Linear Pair - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Two adjacent angles forming a straight line are called:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Linear pair", "D": "Vertical angles"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "Sum of angles in linear pair is:", "options": {"A": "90°", "B": "180°", "C": "270°", "D": "360°"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "If one angle of linear pair is 70°, the other is:", "options": {"A": "20°", "B": "70°", "C": "110°", "D": "290°"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "Linear pair angles are always:", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Acute"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "If two angles form linear pair and one is acute, the other is:", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Straight"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "Angles of linear pair have common:", "options": {"A": "Vertex and arm", "B": "Vertex only", "C": "Arm only", "D": "None"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "If ∠A and ∠B form linear pair and ∠A = 45°, then ∠B = ?", "options": {"A": "45°", "B": "90°", "C": "135°", "D": "180°"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Linear pair postulate states that angles forming linear pair are:", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "If ray stands on line, the two angles formed are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Equal", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Two angles forming linear pair are always:", "options": {"A": "Adjacent", "B": "Non-adjacent", "C": "Vertical", "D": "Opposite"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "If ∠X and ∠Y form linear pair and ∠X = 85°, then ∠Y = ?", "options": {"A": "5°", "B": "85°", "C": "95°", "D": "175°"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "Linear pair angles form a:", "options": {"A": "Right angle", "B": "Straight line", "C": "Complete angle", "D": "Reflex angle"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "If two angles are supplementary and adjacent, they form:", "options": {"A": "Vertical angles", "B": "Linear pair", "C": "Complementary angles", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "One angle of linear pair is 120°. The other is:", "options": {"A": "30°", "B": "60°", "C": "120°", "D": "180°"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "Angles of linear pair share:", "options": {"A": "Common vertex and common arm", "B": "Common vertex only", "C": "Common arm only", "D": "Nothing"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "If two angles form linear pair and one is 90°, the other is:", "options": {"A": "45°", "B": "90°", "C": "135°", "D": "180°"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Linear pair angles are always on the:", "options": {"A": "Same side of transversal", "B": "Opposite sides of line", "C": "Same straight line", "D": "Different lines"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "If ∠P and ∠Q form linear pair, then ∠P + ∠Q = ?", "options": {"A": "90°", "B": "180°", "C": "270°", "D": "360°"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "Which is NOT true about linear pair?", "options": {"A": "They are adjacent", "B": "They sum to 180°", "C": "They are equal", "D": "They form straight line"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "If one angle of linear pair is acute, the other must be:", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Straight"}, "correct_answer": "C"},
    
    {"id": 21, "difficulty": "medium", "question": "If two angles forming linear pair are in ratio 2:3, find both angles.", "options": {"A": "60°, 120°", "B": "72°, 108°", "C": "75°, 105°", "D": "80°, 100°"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "One angle of linear pair is 25° more than the other. Find larger angle.", "options": {"A": "77.5°", "B": "90°", "C": "102.5°", "D": "115°"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "If angles (3x + 10)° and (2x - 20)° form linear pair, find x.", "options": {"A": "30", "B": "35", "C": "38", "D": "42"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "Two angles forming linear pair differ by 40°. Find smaller.", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "If ∠A and ∠B form linear pair and ∠A = 4∠B, find ∠B.", "options": {"A": "30°", "B": "36°", "C": "40°", "D": "45°"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Angles (5x - 15)° and (3x + 25)° form linear pair. Find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Linear pair angles are in ratio 4:5. Find both.", "options": {"A": "60°, 120°", "B": "72°, 108°", "C": "80°, 100°", "D": "85°, 95°"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "One angle is 15° less than twice the other in linear pair. Find larger.", "options": {"A": "65°", "B": "85°", "C": "105°", "D": "115°"}, "correct_answer": "D"},
    {"id": 29, "difficulty": "medium", "question": "If (4x + 20)° and (6x - 40)° form linear pair, find x.", "options": {"A": "18", "B": "20", "C": "22", "D": "24"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Two angles in linear pair differ by 50°. Find smaller.", "options": {"A": "55°", "B": "65°", "C": "75°", "D": "85°"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "If ∠P = 3∠Q and they form linear pair, find ∠P.", "options": {"A": "45°", "B": "90°", "C": "135°", "D": "180°"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "Angles (7x - 25)° and (5x + 15)° form linear pair. Find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Linear pair angles in ratio 5:7. Find smaller.", "options": {"A": "65°", "B": "70°", "C": "75°", "D": "80°"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "One angle is 30° more than half the other in linear pair. Find larger.", "options": {"A": "80°", "B": "100°", "C": "120°", "D": "140°"}, "correct_answer": "D"},
    {"id": 35, "difficulty": "medium", "question": "If (2x + 30)° and (3x - 20)° form linear pair, find x.", "options": {"A": "30", "B": "34", "C": "38", "D": "42"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Two linear pair angles differ by 60°. Find larger.", "options": {"A": "100°", "B": "110°", "C": "120°", "D": "130°"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "If ∠A = 2∠B + 10° and they form linear pair, find ∠B.", "options": {"A": "56.67°", "B": "60°", "C": "63.33°", "D": "66.67°"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Angles (6x - 10)° and (4x + 30)° form linear pair. Find x.", "options": {"A": "12", "B": "15", "C": "16", "D": "18"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "Linear pair angles in ratio 3:4. Find both.", "options": {"A": "60°, 120°", "B": "70°, 110°", "C": "77.14°, 102.86°", "D": "80°, 100°"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "One angle is 40° less than three times the other in linear pair. Find smaller.", "options": {"A": "45°", "B": "50°", "C": "55°", "D": "60°"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "If (3x + 40)° and (5x - 60)° form linear pair, find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "Two linear pair angles differ by 70°. Find smaller.", "options": {"A": "45°", "B": "55°", "C": "65°", "D": "75°"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "If ∠X = 5∠Y - 20° and they form linear pair, find ∠X.", "options": {"A": "130°", "B": "140°", "C": "150°", "D": "160°"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "Angles (8x - 30)° and (6x + 20)° form linear pair. Find x.", "options": {"A": "12", "B": "13.5", "C": "15", "D": "17.5"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "Linear pair angles in ratio 7:8. Find smaller.", "options": {"A": "84°", "B": "90°", "C": "96°", "D": "102°"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "One angle is 50° more than 2/3 of the other in linear pair. Find larger.", "options": {"A": "102°", "B": "108°", "C": "114°", "D": "120°"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "If (4x + 50)° and (6x - 80)° form linear pair, find x.", "options": {"A": "20", "B": "21", "C": "22", "D": "23"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "Two linear pair angles differ by 80°. Find smaller.", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "If ∠M = 4∠N - 30° and they form linear pair, find ∠N.", "options": {"A": "36°", "B": "38°", "C": "40°", "D": "42°"}, "correct_answer": "D"},
    {"id": 50, "difficulty": "medium", "question": "Angles (9x - 40)° and (7x + 20)° form linear pair. Find x.", "options": {"A": "10", "B": "12.5", "C": "15", "D": "17.5"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Linear pair angles in ratio 9:10. Find larger.", "options": {"A": "85°", "B": "90°", "C": "95°", "D": "100°"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "One angle is 60° more than half the other in linear pair. Find smaller.", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "If (5x + 20)° and (7x - 50)° form linear pair, find x.", "options": {"A": "15", "B": "17.5", "C": "20", "D": "22.5"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "Two linear pair angles differ by 90°. Find both.", "options": {"A": "45°, 135°", "B": "50°, 140°", "C": "55°, 145°", "D": "60°, 150°"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "If ∠P = 6∠Q - 45° and they form linear pair, find ∠P.", "options": {"A": "135°", "B": "140°", "C": "145°", "D": "150°"}, "correct_answer": "D"},
    {"id": 56, "difficulty": "medium", "question": "Angles (10x - 60)° and (8x + 40)° form linear pair. Find x.", "options": {"A": "10", "B": "11.11", "C": "12.5", "D": "15"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "Linear pair angles in ratio 11:12. Find smaller.", "options": {"A": "78.26°", "B": "82.17°", "C": "85.71°", "D": "88.24°"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "One angle is 70° more than 3/5 of the other in linear pair. Find larger.", "options": {"A": "110°", "B": "115°", "C": "120°", "D": "125°"}, "correct_answer": "D"},
    {"id": 59, "difficulty": "medium", "question": "If (6x + 30)° and (9x - 60)° form linear pair, find x.", "options": {"A": "12", "B": "14", "C": "16", "D": "18"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Two linear pair angles differ by 100°. Find smaller.", "options": {"A": "30°", "B": "40°", "C": "50°", "D": "60°"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "If ∠A = 7∠B - 60° and they form linear pair, find ∠B.", "options": {"A": "25°", "B": "30°", "C": "35°", "D": "40°"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "Angles (11x - 70)° and (9x + 30)° form linear pair. Find x.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "Linear pair angles in ratio 13:14. Find larger.", "options": {"A": "93.33°", "B": "96.67°", "C": "100°", "D": "103.33°"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "One angle is 80° more than 4/7 of the other in linear pair. Find smaller.", "options": {"A": "60°", "B": "65°", "C": "70°", "D": "75°"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "If (7x + 40)° and (10x - 80)° form linear pair, find x.", "options": {"A": "10", "B": "12.94", "C": "15", "D": "17.06"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "Two linear pair angles differ by 110°. Find both.", "options": {"A": "35°, 145°", "B": "40°, 150°", "C": "45°, 155°", "D": "50°, 160°"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "If ∠X = 8∠Y - 75° and they form linear pair, find ∠X.", "options": {"A": "145°", "B": "150°", "C": "155°", "D": "160°"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "Angles (12x - 80)° and (10x + 60)° form linear pair. Find x.", "options": {"A": "8", "B": "9.09", "C": "10", "D": "11.11"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "Linear pair angles in ratio 15:16. Find smaller.", "options": {"A": "87.1°", "B": "89.03°", "C": "90.97°", "D": "92.9°"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "One angle is 90° more than 5/9 of the other in linear pair. Find larger.", "options": {"A": "120°", "B": "125°", "C": "130°", "D": "135°"}, "correct_answer": "D"},
    {"id": 71, "difficulty": "medium", "question": "If (8x + 50)° and (12x - 100)° form linear pair, find x.", "options": {"A": "10", "B": "11.5", "C": "13", "D": "14.5"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "Two linear pair angles differ by 120°. Find smaller.", "options": {"A": "20°", "B": "30°", "C": "40°", "D": "50°"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "If ∠M = 9∠N - 90° and they form linear pair, find ∠N.", "options": {"A": "25°", "B": "27°", "C": "29°", "D": "31°"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "Angles (13x - 90)° and (11x + 70)° form linear pair. Find x.", "options": {"A": "8", "B": "8.33", "C": "9", "D": "9.5"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "Linear pair angles in ratio 17:18. Find larger.", "options": {"A": "92.57°", "B": "94.29°", "C": "96°", "D": "97.71°"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "One angle is 100° more than 6/11 of the other in linear pair. Find smaller.", "options": {"A": "60°", "B": "65°", "C": "70°", "D": "75°"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "If (9x + 60)° and (15x - 120)° form linear pair, find x.", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "Two linear pair angles differ by 130°. Find both.", "options": {"A": "25°, 155°", "B": "30°, 160°", "C": "35°, 165°", "D": "40°, 170°"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "If ∠P = 10∠Q - 105° and they form linear pair, find ∠P.", "options": {"A": "155°", "B": "160°", "C": "165°", "D": "170°"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "Angles (14x - 100)° and (12x + 80)° form linear pair. Find x.", "options": {"A": "7", "B": "7.69", "C": "8.33", "D": "9"}, "correct_answer": "B"},
    
    {"id": 81, "difficulty": "hard", "question": "If two angles forming linear pair are (x² - 5x)° and (x² + 3x - 10)°, find x.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "In triangle ABC, ∠A and ∠B form linear pair with exterior angle at C. If ∠A = 65°, find ∠C.", "options": {"A": "25°", "B": "35°", "C": "45°", "D": "55°"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "If angles (2x² - 10)° and (3x² - 5x)° form linear pair, find x.", "options": {"A": "2, 5", "B": "3, 6", "C": "4, 7", "D": "5, 8"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Three angles around a point are in ratio 1:2:3. If two of them form linear pair, find all angles.", "options": {"A": "60°, 120°, 180°", "B": "50°, 100°, 150°, 60°", "C": "45°, 90°, 135°, 90°", "D": "40°, 80°, 120°, 120°"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "If linear pair angles satisfy sin(∠A) = cos(∠B), find ∠A and ∠B.", "options": {"A": "45°, 135°", "B": "30°, 150°", "C": "60°, 120°", "D": "90°, 90°"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "In quadrilateral, two adjacent angles form linear pair. If other two angles are 70° and 110°, find the linear pair angles.", "options": {"A": "80°, 100°", "B": "85°, 95°", "C": "90°, 90°", "D": "75°, 105°"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "If (x³ - 8)° and (x² + 2x + 4)° form linear pair, find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Two lines intersect. If one linear pair has angles in ratio 3:5 and other linear pair has angles differing by 40°, find all angles.", "options": {"A": "67.5°, 112.5°, 67.5°, 112.5°", "B": "60°, 120°, 60°, 120°", "C": "70°, 110°, 70°, 110°", "D": "75°, 105°, 75°, 105°"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "If linear pair angles are such that one is 30° more than twice the square of the other's complement, find angles.", "options": {"A": "60°, 120°", "B": "70°, 110°", "C": "80°, 100°", "D": "90°, 90°"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "In pentagon, three consecutive angles form two linear pairs. If middle angle is 120°, find adjacent angles.", "options": {"A": "50°, 70°", "B": "55°, 65°", "C": "60°, 60°", "D": "65°, 55°"}, "correct_answer": "C"},
    {"id": 91, "difficulty": "hard", "question": "If angles (log₂x)° and (log₄x)° form linear pair, find x.", "options": {"A": "4", "B": "8", "C": "16", "D": "32"}, "correct_answer": "C"},
    {"id": 92, "difficulty": "hard", "question": "Two linear pairs share common angle. If other angles are 70° and 130°, find common angle.", "options": {"A": "100°", "B": "110°", "C": "120°", "D": "130°"}, "correct_answer": "B"},
    {"id": 93, "difficulty": "hard", "question": "If (√x + 5)° and (√x + 85)° form linear pair, find x.", "options": {"A": "900", "B": "1600", "C": "2500", "D": "3600"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "In hexagon, four consecutive angles form three linear pairs. If first is 50°, third is 130°, find second and fourth.", "options": {"A": "80°, 100°", "B": "90°, 90°", "C": "85°, 95°", "D": "70°, 110°"}, "correct_answer": "D"},
    {"id": 95, "difficulty": "hard", "question": "If linear pair angles satisfy tan(∠A) = cot(∠B), find ∠A and ∠B.", "options": {"A": "45°, 135°", "B": "30°, 150°", "C": "60°, 120°", "D": "90°, 90°"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Three angles around point sum to 360°. Two form linear pair. If third is 150°, find linear pair angles.", "options": {"A": "95°, 115°", "B": "100°, 110°", "C": "105°, 105°", "D": "90°, 120°"}, "correct_answer": "C"},
    {"id": 97, "difficulty": "hard", "question": "If (2ˣ)° and (2ˣ⁺²)° form linear pair, find x.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "In octagon, five consecutive angles form four linear pairs. If first is 40°, fifth is 140°, find middle three angles.", "options": {"A": "80°, 100°, 80°", "B": "85°, 95°, 85°", "C": "90°, 90°, 90°", "D": "75°, 105°, 75°"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "If linear pair angles are arithmetic and geometric means of 20° and 180° respectively, find angles.", "options": {"A": "80°, 100°", "B": "85°, 95°", "C": "90°, 90°", "D": "95°, 85°"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "Two intersecting lines form two linear pairs. If one angle from first pair and one from second pair sum to 210°, 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"}
  ]
}