{
  "title": "Construction of Angles - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Which angle can be constructed using ruler and compass?", "options": {"A": "10°", "B": "15°", "C": "40°", "D": "50°"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "To construct 60° angle, what is first step?", "options": {"A": "Draw line segment", "B": "Draw arc from point", "C": "Draw perpendicular", "D": "Draw circle"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "90° angle can be constructed by:", "options": {"A": "Bisecting 180°", "B": "Bisecting 60°", "C": "Bisecting 45°", "D": "All of these"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Which angle cannot be constructed exactly with ruler and compass?", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "20°"}, "correct_answer": "D"},
    {"id": 5, "difficulty": "easy", "question": "To construct 30° angle, we first construct:", "options": {"A": "90° angle", "B": "60° angle", "C": "45° angle", "D": "120° angle"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "How to construct 120° angle?", "options": {"A": "Bisect 60°", "B": "Supplement of 60°", "C": "Double 60°", "D": "Bisect 240°"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Which angles can be constructed exactly?", "options": {"A": "Multiples of 15°", "B": "Multiples of 10°", "C": "Multiples of 5°", "D": "Multiples of 1°"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "To construct 75° angle, we add:", "options": {"A": "45° + 30°", "B": "60° + 15°", "C": "90° - 15°", "D": "All of these"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "First step in constructing any angle is:", "options": {"A": "Draw base line", "B": "Mark vertex", "C": "Draw arc", "D": "A and B"}, "correct_answer": "D"},
    {"id": 10, "difficulty": "easy", "question": "Angle of 135° can be obtained by:", "options": {"A": "90° + 45°", "B": "180° - 45°", "C": "60° + 75°", "D": "A and B"}, "correct_answer": "D"},
    {"id": 11, "difficulty": "easy", "question": "Which is correct sequence for 45° construction?", "options": {"A": "90° then bisect", "B": "60° then bisect", "C": "120° then bisect", "D": "30° then double"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "To construct 105° angle, we can use:", "options": {"A": "90° + 15°", "B": "60° + 45°", "C": "120° - 15°", "D": "All of these"}, "correct_answer": "D"},
    {"id": 13, "difficulty": "easy", "question": "Which angle is complement of 30°?", "options": {"A": "60°", "B": "45°", "C": "90°", "D": "150°"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Supplement of 45° is:", "options": {"A": "45°", "B": "90°", "C": "135°", "D": "180°"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "In equilateral triangle, each angle is:", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "Which requires fewest steps: 15° or 30°?", "options": {"A": "15°", "B": "30°", "C": "Both equal", "D": "Cannot compare"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "To construct 22.5° angle, bisect:", "options": {"A": "45°", "B": "90°", "C": "30°", "D": "60°"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Which angle is double of 30°?", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "Angle between minute and hour hand at 3:00 is:", "options": {"A": "30°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "If we bisect 90° twice, we get:", "options": {"A": "22.5°", "B": "45°", "C": "30°", "D": "15°"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Construct 67.5° angle. Which combination works?", "options": {"A": "60° + 7.5°", "B": "45° + 22.5°", "C": "90° - 22.5°", "D": "All of these"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "Construct 52.5° angle. Minimum steps?", "options": {"A": "45° + 7.5°", "B": "60° - 7.5°", "C": "90° - 37.5°", "D": "30° + 22.5°"}, "correct_answer": "D"},
    {"id": 23, "difficulty": "medium", "question": "Construct 7.5° angle. How?", "options": {"A": "Bisect 15°", "B": "Bisect 30° twice", "C": "Bisect 60° thrice", "D": "A and B"}, "correct_answer": "D"},
    {"id": 24, "difficulty": "medium", "question": "Construct 127.5° angle. Which method?", "options": {"A": "180° - 52.5°", "B": "90° + 37.5°", "C": "120° + 7.5°", "D": "All of these"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Construct 112.5° angle using fewest steps.", "options": {"A": "90° + 22.5°", "B": "180° - 67.5°", "C": "135° - 22.5°", "D": "120° - 7.5°"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Construct 82.5° angle. Best approach?", "options": {"A": "90° - 7.5°", "B": "60° + 22.5°", "C": "45° + 37.5°", "D": "75° + 7.5°"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Construct 142.5° angle. Which complement?", "options": {"A": "37.5°", "B": "45°", "C": "52.5°", "D": "67.5°"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Construct angle of 1° is:", "options": {"A": "Possible with ruler/compass", "B": "Not possible exactly", "C": "Possible with protractor only", "D": "Possible with advanced tools"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "Construct 37.5° angle. Minimum bisections needed from constructible angles?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},    {"id": 30, "difficulty": "medium", "question": "Construct 97.5° angle. Use:", "options": {"A": "90° + 7.5°", "B": "120° - 22.5°", "C": "60° + 37.5°", "D": "All of these"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Construct 172.5° angle. Relation to 7.5°?", "options": {"A": "Supplement", "B": "Complement", "C": "Double", "D": "Triple"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Angle 255° can be constructed as:", "options": {"A": "180° + 75°", "B": "270° - 15°", "C": "240° + 15°", "D": "All of these"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Construct 11.25° angle. How many bisections from 90°?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Construct 157.5° angle. Which supplement?", "options": {"A": "22.5°", "B": "32.5°", "C": "42.5°", "D": "52.5°"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Construct 202.5° angle. Express as:", "options": {"A": "180° + 22.5°", "B": "270° - 67.5°", "C": "225° - 22.5°", "D": "A and B"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Construct 292.5° angle. Simplified form?", "options": {"A": "360° - 67.5°", "B": "270° + 22.5°", "C": "300° - 7.5°", "D": "All of these"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Construct 337.5° angle. How?", "options": {"A": "360° - 22.5°", "B": "270° + 67.5°", "C": "315° + 22.5°", "D": "A and B"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Construct angle π/3 radians in degrees:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "Construct angle 2π/3 radians in degrees:", "options": {"A": "90°", "B": "120°", "C": "135°", "D": "150°"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Construct angle 5π/6 radians in degrees:", "options": {"A": "120°", "B": "135°", "C": "150°", "D": "165°"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "Construct 85° angle approximately. Closest constructible angle?", "options": {"A": "84.375°", "B": "85.5°", "C": "86.25°", "D": "87.5°"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Construct 95° angle. Best approximation?", "options": {"A": "93.75°", "B": "95.625°", "C": "96.875°", "D": "97.5°"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Construct angle whose tangent is 1:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "Construct angle whose sine is 1/2:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Construct angle whose cosine is √3/2:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Construct angle in regular pentagon:", "options": {"A": "72°", "B": "108°", "C": "Both A and B", "D": "Neither"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "Construct angle in regular hexagon:", "options": {"A": "60°", "B": "120°", "C": "Both A and B", "D": "Neither"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "Construct angle in regular octagon:", "options": {"A": "45°", "B": "135°", "C": "Both A and B", "D": "Neither"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "Construct 3° angle exactly:", "options": {"A": "Possible", "B": "Not possible", "C": "Possible with special tools", "D": "Possible using trigonometry"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "Construct 18° angle. How?", "options": {"A": "Construct pentagon and bisect 36°", "B": "Trisect 54°", "C": "Both A and B", "D": "Neither is possible"}, "correct_answer": "A"},    {"id": 51, "difficulty": "medium", "question": "Construct 54° angle using pentagon.", "options": {"A": "Possible", "B": "Not possible", "C": "Approximate only", "D": "Using advanced methods"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Construct 108° angle. Related to:", "options": {"A": "Pentagon", "B": "Hexagon", "C": "Octagon", "D": "Decagon"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Construct 144° angle. Related to:", "options": {"A": "Decagon", "B": "Pentagon", "C": "Octagon", "D": "Dodecagon"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Construct 36° angle. How?", "options": {"A": "Bisect 72°", "B": "Construct pentagon", "C": "Golden ratio construction", "D": "All of these"}, "correct_answer": "D"},
    {"id": 55, "difficulty": "medium", "question": "Construct 40° angle exactly:", "options": {"A": "Possible", "B": "Not possible", "C": "Possible approximately", "D": "Possible with marked ruler"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "Construct 140° angle. As supplement of:", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Construct 210° angle. As:", "options": {"A": "180° + 30°", "B": "240° - 30°", "C": "270° - 60°", "D": "A and B"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Construct 330° angle. As:", "options": {"A": "360° - 30°", "B": "270° + 60°", "C": "300° + 30°", "D": "All of these"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Construct angle whose supplement is triple its complement. Measure?", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Construct angle which is its own complement:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "Construct angle which is its own supplement:", "options": {"A": "45°", "B": "90°", "C": "120°", "D": "180°"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "Construct 67°30' angle. In decimal:", "options": {"A": "67.25°", "B": "67.5°", "C": "67.75°", "D": "68°"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "Construct 22°30' angle. As fraction of 90°:", "options": {"A": "1/2", "B": "1/3", "C": "1/4", "D": "1/5"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "Construct 48°45' angle. In decimal degrees:", "options": {"A": "48.5°", "B": "48.6°", "C": "48.75°", "D": "48.8°"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "Construct 125°15' angle. Simplify:", "options": {"A": "125.25°", "B": "125.5°", "C": "125.75°", "D": "126°"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Construct angle whose measure in radians is π/12. In degrees:", "options": {"A": "10°", "B": "12°", "C": "15°", "D": "18°"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "Construct angle whose measure in radians is 3π/8. In degrees:", "options": {"A": "60°", "B": "67.5°", "C": "72°", "D": "75°"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "Construct angle whose measure in radians is 5π/12. In degrees:", "options": {"A": "60°", "B": "65°", "C": "70°", "D": "75°"}, "correct_answer": "D"},
    {"id": 69, "difficulty": "medium", "question": "Construct angle whose measure in radians is 7π/6. In degrees:", "options": {"A": "180°", "B": "210°", "C": "225°", "D": "240°"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "Construct angle whose measure in radians is 11π/12. In degrees:", "options": {"A": "150°", "B": "155°", "C": "160°", "D": "165°"}, "correct_answer": "D"},
    {"id": 71, "difficulty": "medium", "question": "Construct 82°30' angle. How?", "options": {"A": "60° + 22.5°", "B": "90° - 7.5°", "C": "45° + 37.5°", "D": "A and B"}, "correct_answer": "D"},
    {"id": 72, "difficulty": "medium", "question": "Construct 97°30' angle. As:", "options": {"A": "90° + 7.5°", "B": "120° - 22.5°", "C": "60° + 37.5°", "D": "All of these"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Construct 112°30' angle. Use:", "options": {"A": "90° + 22.5°", "B": "135° - 22.5°", "C": "120° - 7.5°", "D": "A and B"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "Construct 157°30' angle. Supplement of:", "options": {"A": "22.5°", "B": "32.5°", "C": "42.5°", "D": "52.5°"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Construct 202°30' angle. As:", "options": {"A": "180° + 22.5°", "B": "225° - 22.5°", "C": "270° - 67.5°", "D": "A and B"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Construct 247°30' angle. As:", "options": {"A": "270° - 22.5°", "B": "225° + 22.5°", "C": "240° + 7.5°", "D": "A and B"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "Construct 292°30' angle. As:", "options": {"A": "270° + 22.5°", "B": "360° - 67.5°", "C": "300° - 7.5°", "D": "All of these"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Construct 337°30' angle. As:", "options": {"A": "360° - 22.5°", "B": "315° + 22.5°", "C": "330° + 7.5°", "D": "A and B"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Construct angle whose complement is 20°. Measure?", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "Construct angle whose supplement is 100°. Measure?", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "C"},
    {"id": 81, "difficulty": "hard", "question": "Construct 3π/7 radians angle exactly:", "options": {"A": "Possible", "B": "Not possible", "C": "Approximately 77.14°", "D": "B and C"}, "correct_answer": "D"},
    {"id": 82, "difficulty": "hard", "question": "Construct angle of 1 radian exactly:", "options": {"A": "Possible", "B": "Not possible", "C": "Approximately 57.3°", "D": "B and C"}, "correct_answer": "D"},
    {"id": 83, "difficulty": "hard", "question": "Construct angle whose sine is 1/√2:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "Construct angle whose cosine is 1/√2:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 85, "difficulty": "hard", "question": "Construct angle whose tangent is √3:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "Construct angle whose cotangent is 1:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "Construct angle whose secant is 2:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "Construct angle whose cosecant is √2:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "Construct angle equal to sum of angles of pentagon and hexagon:", "options": {"A": "540° + 720° = 1260°", "B": "108° + 120° = 228°", "C": "Reduce to 48°", "D": "B and C"}, "correct_answer": "D"},
   {"id": 90, "difficulty": "hard", "question": "Construct angle of regular 17-gon:", "options": {"A": "Approximately 21.176°", "B": "Exactly constructible", "C": "Not constructible", "D": "A and B"}, "correct_answer": "D"},    {"id": 91, "difficulty": "hard", "question": "Construct angle of regular 7-gon:", "options": {"A": "Approximately 51.428°", "B": "Exactly constructible", "C": "Not constructible", "D": "A and C"}, "correct_answer": "D"},
    {"id": 92, "difficulty": "hard", "question": "Construct angle of regular 9-gon:", "options": {"A": "40°", "B": "Exactly constructible", "C": "Not constructible", "D": "A and C"}, "correct_answer": "D"},
    {"id": 93, "difficulty": "hard", "question": "Construct angle whose measure in degrees is algebraic number but not constructible:", "options": {"A": "20°", "B": "40°", "C": "60°", "D": "80°"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "Construct angle trisecting 60°:", "options": {"A": "Possible", "B": "Not possible", "C": "Gives 20° approximately", "D": "B and C"}, "correct_answer": "D"},
   {"id": 95, "difficulty": "hard", "question": "Construct angle bisecting 10°:", "options": {"A": "Possible", "B": "Not possible", "C": "Gives 5°", "D": "A and C"}, "correct_answer": "B"},    {"id": 96, "difficulty": "hard", "question": "Construct angle whose measure is golden ratio φ times 45°:", "options": {"A": "Approximately 72.9°", "B": "Exactly constructible", "C": "Not constructible", "D": "A and C"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Construct angle equal to arcsin(3/5):", "options": {"A": "Approximately 36.87°", "B": "Exactly constructible", "C": "Not constructible", "D": "A and B"}, "correct_answer": "D"},
    {"id": 98, "difficulty": "hard", "question": "Construct angle equal to arctan(4/3):", "options": {"A": "Approximately 53.13°", "B": "Exactly constructible", "C": "Not constructible", "D": "A and B"}, "correct_answer": "D"},
    {"id": 99, "difficulty": "hard", "question": "Construct angle whose supplement is to complement as 5:2. Measure?", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Construct angle which divided by its complement gives quotient 2. Measure?", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "C"}
  ]
}