{
  "title": "Linear Pair - Grade 7 CBSE",
  "total_questions": 150,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "A linear pair consists of:", "options": {"A": "Two acute angles", "B": "Two right angles", "C": "Two adjacent angles whose sum is 180°", "D": "Two vertical angles"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "Angles in a linear pair are always:", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Vertical"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "If two angles form a linear pair and one angle is 60°, the other is:", "options": {"A": "30°", "B": "60°", "C": "120°", "D": "300°"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "Angles in a linear pair have a common:", "options": {"A": "Vertex and arm", "B": "Vertex only", "C": "Arm only", "D": "Neither vertex nor arm"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "If ∠A and ∠B form a linear pair and ∠A = 90°, then ∠B =", "options": {"A": "45°", "B": "90°", "C": "180°", "D": "270°"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Two angles forming a linear pair are always:", "options": {"A": "Equal", "B": "Adjacent", "C": "Vertically opposite", "D": "Complementary"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "If two angles are supplementary and adjacent, they form:", "options": {"A": "Vertical angles", "B": "A linear pair", "C": "Complementary angles", "D": "Corresponding angles"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "In a linear pair, the non-common arms are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Opposite rays", "D": "Equal"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "If one angle of a linear pair is acute, the other must be:", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Straight"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "The sum of angles in a linear pair is:", "options": {"A": "90°", "B": "180°", "C": "270°", "D": "360°"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "If two angles form a linear pair and one is 45°, the other is:", "options": {"A": "45°", "B": "90°", "C": "135°", "D": "225°"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "Angles in a linear pair are on the:", "options": {"A": "Same side of a line", "B": "Opposite sides of a line", "C": "Same line", "D": "Parallel lines"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "If two angles are a linear pair, their non-common arms form:", "options": {"A": "An acute angle", "B": "A straight line", "C": "A right angle", "D": "Parallel lines"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Can two obtuse angles form a linear pair?", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Only if they are equal"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If ∠P and ∠Q form a linear pair and ∠P = 110°, then ∠Q is:", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Straight"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Two angles that form a linear pair are always:", "options": {"A": "Congruent", "B": "Supplementary", "C": "Complementary", "D": "Vertical"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "If one angle of a linear pair is 75°, the other is:", "options": {"A": "15°", "B": "75°", "C": "105°", "D": "285°"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "Can two right angles form a linear pair?", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Only if adjacent"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "In a linear pair, the angles share:", "options": {"A": "Only a vertex", "B": "Only a ray", "C": "A vertex and a ray", "D": "Neither vertex nor ray"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "If ∠A and ∠B are a linear pair, which equation is always true?", "options": {"A": "∠A = ∠B", "B": "∠A + ∠B = 90°", "C": "∠A + ∠B = 180°", "D": "∠A - ∠B = 90°"}, "correct_answer": "C"},

    {"id": 21, "difficulty": "medium", "question": "If two angles forming a linear pair are in the ratio 2:3, find the larger angle.", "options": {"A": "72°", "B": "90°", "C": "108°", "D": "120°"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "∠A and ∠B form a linear pair. If ∠A = (2x + 30)° and ∠B = (3x - 10)°, find ∠A.", "options": {"A": "70°", "B": "82°", "C": "98°", "D": "110°"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Two angles form a linear pair. If one angle is 20° less than three times the other, find the smaller angle.", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "In the figure, ∠AOC and ∠BOC form a linear pair. If ∠AOC = 70°, find ∠BOC.", "options": {"A": "20°", "B": "70°", "C": "110°", "D": "290°"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "If two angles forming a linear pair are equal, each angle measures:", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "180°"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "∠P and ∠Q form a linear pair. If ∠P = (4x - 15)° and ∠Q = (x + 60)°, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "27"}, "correct_answer": "D"},
    {"id": 27, "difficulty": "medium", "question": "Two angles are in ratio 5:4 and form a linear pair. Find the difference between them.", "options": {"A": "10°", "B": "20°", "C": "30°", "D": "40°"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "If one angle of a linear pair is 15° more than twice the other, find the larger angle.", "options": {"A": "55°", "B": "85°", "C": "125°", "D": "145°"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "In the figure, ray OA and ray OB are opposite rays. If ∠AOC = 40°, find ∠BOC.", "options": {"A": "40°", "B": "50°", "C": "140°", "D": "180°"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "∠X and ∠Y form a linear pair. If ∠X = 2∠Y + 30°, find ∠Y.", "options": {"A": "30°", "B": "50°", "C": "70°", "D": "110°"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Two angles forming a linear pair are such that one is 60° more than the other. Find both angles.", "options": {"A": "60°, 120°", "B": "70°, 110°", "C": "80°, 100°", "D": "90°, 90°"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "If ∠A and ∠B form a linear pair and ∠A = (5x + 10)°, ∠B = (3x + 30)°, find ∠B.", "options": {"A": "60°", "B": "75°", "C": "90°", "D": "105°"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "The difference between two angles forming a linear pair is 40°. Find the smaller angle.", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "In the figure, ∠POR and ∠ROQ form a linear pair. If ∠POR = 85°, find ∠ROQ.", "options": {"A": "5°", "B": "85°", "C": "95°", "D": "275°"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "If two angles forming a linear pair are in ratio 7:5, find the angles.", "options": {"A": "75°, 105°", "B": "70°, 110°", "C": "105°, 75°", "D": "110°, 70°"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "∠M and ∠N form a linear pair. If ∠M = 3∠N - 20°, find ∠M.", "options": {"A": "70°", "B": "100°", "C": "110°", "D": "130°"}, "correct_answer": "D"},
    {"id": 37, "difficulty": "medium", "question": "Two angles are such that they form a linear pair. If one is 45° less than the other, find the larger angle.", "options": {"A": "67.5°", "B": "90°", "C": "112.5°", "D": "135°"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "In the figure, ray OP and ray OQ are opposite rays. If ∠ROP = 55°, find ∠SOQ if ∠ROS = 90°.", "options": {"A": "35°", "B": "55°", "C": "125°", "D": "145°"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "If ∠A and ∠B form a linear pair and ∠A = (2x + 50)°, ∠B = (3x - 10)°, find x.", "options": {"A": "20", "B": "24", "C": "28", "D": "32"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "Two angles forming a linear pair are such that twice one angle is equal to three times the other. Find the smaller angle.", "options": {"A": "54°", "B": "72°", "C": "108°", "D": "144°"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "In the figure, ∠AOB and ∠BOC form a linear pair. If ∠AOB = 120°, find ∠BOC.", "options": {"A": "30°", "B": "60°", "C": "120°", "D": "240°"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "∠P and ∠Q form a linear pair. If ∠P = 4∠Q + 10°, find ∠Q.", "options": {"A": "28°", "B": "34°", "C": "38°", "D": "42°"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "The sum of two angles forming a linear pair is 180°. If one angle is 25° more than the other, find both.", "options": {"A": "65°, 115°", "B": "70°, 110°", "C": "75°, 105°", "D": "77.5°, 102.5°"}, "correct_answer": "D"},
    {"id": 44, "difficulty": "medium", "question": "In the figure, ray OX and ray OY are opposite rays. If ∠XOZ = 30°, find ∠YOZ.", "options": {"A": "30°", "B": "60°", "C": "150°", "D": "180°"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "If two angles forming a linear pair are in ratio 8:7, find the difference between them.", "options": {"A": "8°", "B": "10°", "C": "12°", "D": "15°"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "∠X and ∠Y form a linear pair. If ∠X = (5x - 20)° and ∠Y = (2x + 40)°, find ∠X.", "options": {"A": "80°", "B": "100°", "C": "120°", "D": "140°"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "Two angles are such that they form a linear pair. If one angle is three times the other, find the smaller angle.", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "In the figure, ∠AOC and ∠COB form a linear pair. If ∠AOC = 2∠COB, find ∠COB.", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "If ∠P and ∠Q form a linear pair and ∠P = (3x + 15)°, ∠Q = (2x + 45)°, find x.", "options": {"A": "20", "B": "22", "C": "24", "D": "26"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "Two angles forming a linear pair are such that five times one angle is equal to four times the other. Find the larger angle.", "options": {"A": "80°", "B": "90°", "C": "100°", "D": "110°"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "medium", "question": "In the figure, ray OM and ray ON are opposite rays. If ∠LOM = 65°, find ∠LON.", "options": {"A": "65°", "B": "115°", "C": "245°", "D": "295°"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "∠A and ∠B form a linear pair. If ∠A = 2∠B - 30°, find ∠B.", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "The difference between two angles forming a linear pair is 60°. Find the angles.", "options": {"A": "50°, 110°", "B": "60°, 120°", "C": "70°, 130°", "D": "80°, 140°"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "In the figure, ∠POQ and ∠QOR form a linear pair. If ∠POQ = 110°, find ∠QOR.", "options": {"A": "20°", "B": "70°", "C": "110°", "D": "250°"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "If two angles forming a linear pair are in ratio 11:9, find the larger angle.", "options": {"A": "81°", "B": "90°", "C": "99°", "D": "110°"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "∠M and ∠N form a linear pair. If ∠M = (6x - 10)° and ∠N = (4x + 30)°, find ∠M.", "options": {"A": "70°", "B": "80°", "C": "90°", "D": "110°"}, "correct_answer": "D"},
    {"id": 57, "difficulty": "medium", "question": "Two angles are such that they form a linear pair. If one angle is 35° more than half the other, find the larger angle.", "options": {"A": "70°", "B": "90°", "C": "110°", "D": "130°"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "In the figure, ray OA and ray OB are opposite rays. If ∠AOC = 75° and ∠BOD = 105°, find ∠COD.", "options": {"A": "30°", "B": "75°", "C": "105°", "D": "180°"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "If ∠A and ∠B form a linear pair and ∠A = (4x + 20)°, ∠B = (x + 70)°, find x.", "options": {"A": "15", "B": "18", "C": "21", "D": "24"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Two angles forming a linear pair are such that seven times one angle is equal to eight times the other. Find the smaller angle.", "options": {"A": "72°", "B": "84°", "C": "96°", "D": "108°"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "In the figure, ∠XOY and ∠YOZ form a linear pair. If ∠XOY = 135°, find ∠YOZ.", "options": {"A": "35°", "B": "45°", "C": "55°", "D": "65°"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "∠P and ∠Q form a linear pair. If ∠P = 5∠Q - 60°, find ∠Q.", "options": {"A": "30°", "B": "40°", "C": "50°", "D": "60°"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "The sum of two angles forming a linear pair is 180°. If one angle is 40° less than the other, find both.", "options": {"A": "60°, 120°", "B": "70°, 110°", "C": "80°, 100°", "D": "90°, 90°"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "In the figure, ray OP and ray OQ are opposite rays. If ∠ROP = 48°, find ∠SOQ if ∠ROS = 90°.", "options": {"A": "42°", "B": "48°", "C": "132°", "D": "138°"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "If two angles forming a linear pair are in ratio 13:11, find the difference between them.", "options": {"A": "10°", "B": "12°", "C": "15°", "D": "18°"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "∠X and ∠Y form a linear pair. If ∠X = (7x - 30)° and ∠Y = (3x + 50)°, find ∠X.", "options": {"A": "100°", "B": "110°", "C": "120°", "D": "130°"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "Two angles are such that they form a linear pair. If one angle is 50° more than the other, find the smaller angle.", "options": {"A": "55°", "B": "60°", "C": "65°", "D": "70°"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "In the figure, ∠AOB and ∠BOC form a linear pair. If ∠AOB = 100°, find ∠BOC.", "options": {"A": "40°", "B": "80°", "C": "100°", "D": "260°"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "If ∠P and ∠Q form a linear pair and ∠P = (5x + 25)°, ∠Q = (2x + 65)°, find x.", "options": {"A": "10", "B": "12", "C": "14", "D": "16"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "Two angles forming a linear pair are such that nine times one angle is equal to ten times the other. Find the larger angle.", "options": {"A": "90°", "B": "95°", "C": "100°", "D": "105°"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "In the figure, ray OX and ray OY are opposite rays. If ∠XOZ = 35°, find ∠YOZ.", "options": {"A": "35°", "B": "55°", "C": "145°", "D": "180°"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "∠A and ∠B form a linear pair. If ∠A = 6∠B - 50°, find ∠B.", "options": {"A": "30°", "B": "32°", "C": "34°", "D": "36°"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "The difference between two angles forming a linear pair is 80°. Find the angles.", "options": {"A": "40°, 120°", "B": "50°, 130°", "C": "60°, 140°", "D": "70°, 150°"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "In the figure, ∠POR and ∠ROQ form a linear pair. If ∠POR = 95°, find ∠ROQ.", "options": {"A": "5°", "B": "85°", "C": "95°", "D": "265°"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "If two angles forming a linear pair are in ratio 17:13, find the larger angle.", "options": {"A": "85°", "B": "95°", "C": "102°", "D": "110°"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "∠M and ∠N form a linear pair. If ∠M = (8x - 20)° and ∠N = (2x + 60)°, find ∠M.", "options": {"A": "100°", "B": "110°", "C": "120°", "D": "130°"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Two angles are such that they form a linear pair. If one angle is 55° more than one-third the other, find the larger angle.", "options": {"A": "105°", "B": "115°", "C": "125°", "D": "135°"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "In the figure, ray OA and ray OB are opposite rays. If ∠AOC = 85° and ∠BOD = 95°, find ∠COD.", "options": {"A": "10°", "B": "85°", "C": "95°", "D": "180°"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "If ∠A and ∠B form a linear pair and ∠A = (6x + 30)°, ∠B = (x + 50)°, find x.", "options": {"A": "12", "B": "14", "C": "16", "D": "18"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "Two angles forming a linear pair are such that eleven times one angle is equal to twelve times the other. Find the smaller angle.", "options": {"A": "72°", "B": "78°", "C": "84°", "D": "90°"}, "correct_answer": "C"},

    {"id": 81, "difficulty": "hard", "question": "In the figure, ray OP, ray OQ, ray OR, and ray OS are such that ∠POQ and ∠QOR form a linear pair, and ∠QOR and ∠ROS form another linear pair. If ∠POQ = 60°, find ∠ROS.", "options": {"A": "30°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "D"},
    {"id": 82, "difficulty": "hard", "question": "Three rays OA, OB, and OC are such that ∠AOB and ∠BOC form a linear pair, and ∠AOC = 120°. If ∠AOB = 2∠BOC, find ∠BOC.", "options": {"A": "30°", "B": "40°", "C": "50°", "D": "60°"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "If two linear pairs share a common arm and the non-common arms are perpendicular, find the measure of each angle in the first linear pair if one angle is 40°.", "options": {"A": "40°, 140°, 50°, 130°", "B": "40°, 140°, 40°, 140°", "C": "40°, 140°, 90°, 90°", "D": "40°, 140°, 60°, 120°"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "In the figure, rays OA, OB, OC, and OD are such that ∠AOB and ∠BOC form a linear pair, ∠BOC and ∠COD form a linear pair. If ∠AOB = 70° and ∠COD = 50°, find ∠BOC.", "options": {"A": "60°", "B": "90°", "C": "110°", "D": "120°"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "If ∠A and ∠B form a linear pair, and ∠C and ∠D form another linear pair with the same vertex. If ∠A = 2∠C and ∠B = 3∠D, find ∠A.", "options": {"A": "60°", "B": "72°", "C": "84°", "D": "96°"}, "correct_answer": "B"},
    {"id": 86, "difficulty": "hard", "question": "Four rays OA, OB, OC, OD are such that ∠AOB and ∠BOC form a linear pair, ∠BOC and ∠COD form a linear pair, and ∠AOD = 180°. If ∠AOB = 80°, find ∠COD.", "options": {"A": "20°", "B": "40°", "C": "60°", "D": "80°"}, "correct_answer": "D"},
    {"id": 87, "difficulty": "hard", "question": "In the figure, rays OP, OQ, OR, OS are such that ∠POQ, ∠QOR, and ∠ROS form consecutive linear pairs. If ∠POQ = 50° and ∠ROS = 70°, find ∠QOR.", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "If two linear pairs have a common vertex and their non-common arms are opposite rays, and one angle from first pair is 65°, find all four angles.", "options": {"A": "65°, 115°, 65°, 115°", "B": "65°, 115°, 25°, 155°", "C": "65°, 115°, 90°, 90°", "D": "65°, 115°, 70°, 110°"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Three linear pairs share a common vertex. The sum of the smallest angles from each pair is 150°. If these smallest angles are in arithmetic progression, find the largest of these smallest angles.", "options": {"A": "50°", "B": "55°", "C": "60°", "D": "65°"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "In the figure, rays OA, OB, OC, OD, OE are such that ∠AOB and ∠BOC form linear pair, ∠BOC and ∠COD form linear pair, ∠COD and ∠DOE form linear pair. If ∠AOB = 40° and ∠DOE = 30°, find ∠BOC.", "options": {"A": "70°", "B": "80°", "C": "90°", "D": "100°"}, "correct_answer": "D"},
    {"id": 91, "difficulty": "hard", "question": "If ∠A and ∠B form a linear pair, ∠B and ∠C form a linear pair, and ∠C and ∠D form a linear pair. If ∠A = 50° and ∠D = 40°, find ∠B.", "options": {"A": "90°", "B": "100°", "C": "110°", "D": "130°"}, "correct_answer": "D"},
    {"id": 92, "difficulty": "hard", "question": "In quadrilateral ABCD, ∠A and ∠B form a linear pair, ∠B and ∠C form a linear pair. If ∠A = 70°, find ∠D.", "options": {"A": "70°", "B": "90°", "C": "110°", "D": "130°"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "If three linear pairs share a common vertex and the six angles are in arithmetic progression with common difference 10°, find the smallest angle.", "options": {"A": "20°", "B": "25°", "C": "30°", "D": "35°"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "Rays OA, OB, OC, OD are such that ∠AOB and ∠BOC form linear pair, ∠AOC and ∠COD form linear pair. If ∠AOB = 60° and ∠COD = 50°, find ∠BOC.", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "If ∠P and ∠Q form linear pair, ∠Q and ∠R form linear pair, and ∠P = 2∠R, find ∠Q.", "options": {"A": "60°", "B": "72°", "C": "84°", "D": "96°"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "In the figure, rays OP, OQ, OR, OS, OT are such that consecutive angles form linear pairs. If ∠POQ = 30°, ∠QOR = 50°, ∠ROS = 70°, find ∠SOT.", "options": {"A": "20°", "B": "30°", "C": "40°", "D": "50°"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "If four linear pairs share a common vertex and the eight angles are such that each linear pair has angles in ratio 2:3, 3:4, 4:5, 5:6 respectively, find the smallest angle among all.", "options": {"A": "36°", "B": "40°", "C": "45°", "D": "48°"}, "correct_answer": "D"},
    {"id": 98, "difficulty": "hard", "question": "Rays OA, OB, OC, OD, OE form consecutive linear pairs. If ∠AOB = 20°, ∠BOC = 40°, ∠COD = 60°, find ∠DOE.", "options": {"A": "40°", "B": "60°", "C": "80°", "D": "100°"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "If ∠X and ∠Y form linear pair, ∠Y and ∠Z form linear pair, and ∠Z and ∠W form linear pair. If ∠X = 30° and ∠W = 50°, find ∠Y.", "options": {"A": "100°", "B": "110°", "C": "120°", "D": "130°"}, "correct_answer": "D"},
    {"id": 100, "difficulty": "hard", "question": "In pentagon ABCDE, ∠A and ∠B form linear pair, ∠B and ∠C form linear pair, ∠C and ∠D form linear pair, ∠D and ∠E form linear pair. If ∠A = 60°, find ∠E.", "options": {"A": "60°", "B": "90°", "C": "120°", "D": "150°"}, "correct_answer": "C"}
  ,
  {"id":101,"difficulty":"easy","question":"If two angles form a linear pair, their sum is always:","options":{"A":"90°","B":"120°","C":"180°","D":"360°"},"correct_answer":"C"},
    {"id":102,"difficulty":"easy","question":"A linear pair of angles must be:","options":{"A":"Vertical","B":"Adjacent","C":"Equal","D":"Complementary"},"correct_answer":"B"},
    {"id":103,"difficulty":"easy","question":"If one angle of a linear pair is 35°, the other angle is:","options":{"A":"35°","B":"55°","C":"145°","D":"180°"},"correct_answer":"C"},
    {"id":104,"difficulty":"easy","question":"The non-common arms of a linear pair form:","options":{"A":"A right angle","B":"Parallel lines","C":"Opposite rays","D":"An acute angle"},"correct_answer":"C"},
    {"id":105,"difficulty":"easy","question":"If two angles are adjacent and supplementary, they form:","options":{"A":"Vertical angles","B":"A linear pair","C":"Corresponding angles","D":"Alternate angles"},"correct_answer":"B"},
    {"id":106,"difficulty":"easy","question":"Can two right angles form a linear pair?","options":{"A":"Yes","B":"No","C":"Sometimes","D":"Only if vertical"},"correct_answer":"A"},
    {"id":107,"difficulty":"easy","question":"If one angle in a linear pair is obtuse, the other angle is:","options":{"A":"Acute","B":"Right","C":"Obtuse","D":"Reflex"},"correct_answer":"A"},
    {"id":108,"difficulty":"easy","question":"Angles in a linear pair always share a common:","options":{"A":"Vertex only","B":"Side only","C":"Vertex and one arm","D":"Line"},"correct_answer":"C"},
    {"id":109,"difficulty":"easy","question":"If ∠A and ∠B form a linear pair and ∠A = 90°, then ∠B equals:","options":{"A":"45°","B":"90°","C":"135°","D":"180°"},"correct_answer":"B"},
    {"id":110,"difficulty":"easy","question":"Which statement is always true for a linear pair?","options":{"A":"Angles are equal","B":"Angles are adjacent","C":"Angles are vertical","D":"Angles are complementary"},"correct_answer":"B"},

    {"id":111,"difficulty":"medium","question":"Two angles form a linear pair. If their ratio is 3:7, find the smaller angle.","options":{"A":"36°","B":"42°","C":"54°","D":"63°"},"correct_answer":"B"},
    {"id":112,"difficulty":"medium","question":"∠A and ∠B form a linear pair. If ∠A = (3x + 20)° and ∠B = (5x - 40)°, find x.","options":{"A":"10","B":"15","C":"20","D":"25"},"correct_answer":"B"},
    {"id":113,"difficulty":"medium","question":"If two angles forming a linear pair differ by 40°, find the larger angle.","options":{"A":"70°","B":"90°","C":"110°","D":"130°"},"correct_answer":"C"},
    {"id":114,"difficulty":"medium","question":"Two angles form a linear pair. If one angle is twice the other, find the smaller angle.","options":{"A":"45°","B":"60°","C":"75°","D":"90°"},"correct_answer":"B"},
    {"id":115,"difficulty":"medium","question":"∠P and ∠Q form a linear pair. If ∠P = 4∠Q, find ∠Q.","options":{"A":"30°","B":"36°","C":"45°","D":"60°"},"correct_answer":"B"},
    {"id":116,"difficulty":"medium","question":"If one angle of a linear pair is 25° more than the other, find the smaller angle.","options":{"A":"65°","B":"77.5°","C":"87.5°","D":"95°"},"correct_answer":"B"},
    {"id":117,"difficulty":"medium","question":"The difference of two angles forming a linear pair is 20°. Find the angles.","options":{"A":"80° and 100°","B":"70° and 110°","C":"60° and 120°","D":"50° and 130°"},"correct_answer":"A"},
    {"id":118,"difficulty":"medium","question":"If ∠A and ∠B form a linear pair and ∠A = (2x + 40)°, ∠B = (4x - 20)°, find ∠A.","options":{"A":"60°","B":"80°","C":"100°","D":"120°"},"correct_answer":"B"},
    {"id":119,"difficulty":"medium","question":"Two angles forming a linear pair are such that three times one angle equals twice the other. Find the smaller angle.","options":{"A":"60°","B":"72°","C":"90°","D":"108°"},"correct_answer":"B"},
    {"id":120,"difficulty":"medium","question":"If one angle in a linear pair is acute, the other must be:","options":{"A":"Acute","B":"Right","C":"Obtuse","D":"Reflex"},"correct_answer":"C"},

    {"id":121,"difficulty":"medium","question":"Two angles forming a linear pair are in the ratio 5:7. Find the larger angle.","options":{"A":"75°","B":"90°","C":"105°","D":"120°"},"correct_answer":"C"},
    {"id":122,"difficulty":"medium","question":"∠X and ∠Y form a linear pair. If ∠X = (6x - 30)° and ∠Y = (4x + 10)°, find x.","options":{"A":"10","B":"15","C":"20","D":"25"},"correct_answer":"C"},
    {"id":123,"difficulty":"medium","question":"If two angles forming a linear pair are equal, each angle measures:","options":{"A":"45°","B":"60°","C":"90°","D":"120°"},"correct_answer":"C"},
    {"id":124,"difficulty":"medium","question":"Two angles form a linear pair. If one angle is 3 times the other minus 20°, find the smaller angle.","options":{"A":"40°","B":"50°","C":"60°","D":"70°"},"correct_answer":"B"},
    {"id":125,"difficulty":"medium","question":"The sum of two angles forming a linear pair is 180°. If their ratio is 4:5, find the smaller angle.","options":{"A":"72°","B":"80°","C":"90°","D":"100°"},"correct_answer":"A"},
    {"id":126,"difficulty":"medium","question":"∠A and ∠B form a linear pair. If ∠A = 5∠B − 30°, find ∠B.","options":{"A":"30°","B":"36°","C":"42°","D":"48°"},"correct_answer":"B"},
    {"id":127,"difficulty":"medium","question":"Two angles forming a linear pair differ by 60°. Find the smaller angle.","options":{"A":"50°","B":"60°","C":"70°","D":"80°"},"correct_answer":"B"},
    {"id":128,"difficulty":"medium","question":"If one angle of a linear pair is 15° less than twice the other, find the larger angle.","options":{"A":"95°","B":"105°","C":"115°","D":"125°"},"correct_answer":"C"},
    {"id":129,"difficulty":"medium","question":"∠P and ∠Q form a linear pair. If ∠P + ∠Q = 180° and ∠P − ∠Q = 40°, find ∠P.","options":{"A":"70°","B":"90°","C":"110°","D":"130°"},"correct_answer":"C"},
    {"id":130,"difficulty":"medium","question":"If two angles form a linear pair and one is 4 times the other, find the smaller angle.","options":{"A":"30°","B":"36°","C":"45°","D":"60°"},"correct_answer":"B"},

    {"id":131,"difficulty":"hard","question":"Three consecutive angles form linear pairs at a point. If the first angle is 40° and the third is 60°, find the second angle.","options":{"A":"80°","B":"90°","C":"100°","D":"110°"},"correct_answer":"B"},
    {"id":132,"difficulty":"hard","question":"Two linear pairs share a common arm. If one angle is 70°, find all possible angles.","options":{"A":"70°,110°,70°,110°","B":"70°,110°,90°,90°","C":"70°,110°,80°,100°","D":"70°,110°,60°,120°"},"correct_answer":"A"},
    {"id":133,"difficulty":"hard","question":"Four angles around a point form two linear pairs. If one angle is 55°, find the vertically opposite angle.","options":{"A":"55°","B":"65°","C":"125°","D":"145°"},"correct_answer":"A"},
    {"id":134,"difficulty":"hard","question":"Three linear pairs share a common vertex. If the smallest angles are in ratio 2:3:4 and their sum is 180°, find the largest small angle.","options":{"A":"40°","B":"60°","C":"80°","D":"100°"},"correct_answer":"C"},
    {"id":135,"difficulty":"hard","question":"Two angles form a linear pair. If one angle is 25° more than half the other, find the larger angle.","options":{"A":"95°","B":"105°","C":"115°","D":"125°"},"correct_answer":"C"},
    {"id":136,"difficulty":"hard","question":"If ∠A, ∠B, and ∠C form consecutive linear pairs and ∠A = 30°, ∠C = 50°, find ∠B.","options":{"A":"80°","B":"90°","C":"100°","D":"110°"},"correct_answer":"B"},
    {"id":137,"difficulty":"hard","question":"Two angles forming a linear pair are such that five times one equals seven times the other. Find the larger angle.","options":{"A":"90°","B":"100°","C":"105°","D":"112°"},"correct_answer":"C"},
    {"id":138,"difficulty":"hard","question":"Four rays form four angles at a point. If two adjacent angles form a linear pair and one is 68°, find all angles.","options":{"A":"68°,112°,68°,112°","B":"68°,90°,68°,134°","C":"68°,112°,90°,90°","D":"68°,100°,80°,112°"},"correct_answer":"A"},
    {"id":139,"difficulty":"hard","question":"If the difference between two angles forming a linear pair is 90°, find the smaller angle.","options":{"A":"45°","B":"50°","C":"60°","D":"75°"},"correct_answer":"A"},
    {"id":140,"difficulty":"hard","question":"Three linear pairs are formed at a point. If the smallest angle is 30° and angles increase uniformly, find the largest angle.","options":{"A":"90°","B":"100°","C":"110°","D":"120°"},"correct_answer":"C"},

    {"id":141,"difficulty":"hard","question":"If two linear pairs share a vertex and one angle from each pair is 65°, find the remaining angles.","options":{"A":"65°,115°,65°,115°","B":"65°,125°,55°,115°","C":"65°,115°,90°,90°","D":"65°,115°,70°,110°"},"correct_answer":"A"},
    {"id":142,"difficulty":"hard","question":"The sum of three smallest angles from three linear pairs is 150°. If they are in arithmetic progression, find the largest.","options":{"A":"50°","B":"55°","C":"60°","D":"65°"},"correct_answer":"C"},
    {"id":143,"difficulty":"hard","question":"If two angles form a linear pair and the ratio of their measures is 9:11, find the smaller angle.","options":{"A":"72°","B":"81°","C":"90°","D":"99°"},"correct_answer":"B"},
    {"id":144,"difficulty":"hard","question":"Four consecutive linear pairs are formed around a point. If one angle is 20°, find the angle opposite to it.","options":{"A":"20°","B":"80°","C":"160°","D":"180°"},"correct_answer":"A"},
    {"id":145,"difficulty":"hard","question":"If ∠A and ∠B form a linear pair and ∠A = 2∠B + 10°, find ∠B.","options":{"A":"40°","B":"50°","C":"60°","D":"70°"},"correct_answer":"B"},
    {"id":146,"difficulty":"hard","question":"Three rays form two linear pairs. If the two non-common angles are equal and their sum is 180°, find each.","options":{"A":"45°","B":"60°","C":"90°","D":"120°"},"correct_answer":"C"},
    {"id":147,"difficulty":"hard","question":"If two angles forming a linear pair are such that the larger exceeds the smaller by 100°, find the larger angle.","options":{"A":"110°","B":"120°","C":"140°","D":"150°"},"correct_answer":"C"},
    {"id":148,"difficulty":"hard","question":"Four angles form two linear pairs at a point. If one angle is 35°, find the angle adjacent to its vertically opposite angle.","options":{"A":"35°","B":"55°","C":"145°","D":"165°"},"correct_answer":"C"},
    {"id":149,"difficulty":"hard","question":"If the angles in three linear pairs are in the ratio 2:3:4, find the largest angle.","options":{"A":"80°","B":"90°","C":"100°","D":"120°"},"correct_answer":"D"},
    {"id":150,"difficulty":"hard","question":"Two angles forming a linear pair are such that the sum of their squares is minimum. Find the angles.","options":{"A":"45° and 135°","B":"60° and 120°","C":"90° and 90°","D":"75° and 105°"},"correct_answer":"C"}
  ]
}