{
  "title": "Adjacent angles (Lines and Angles) - Grade 9 CBSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "What are adjacent angles?",
      "options": {
        "A": "Angles that share a common vertex and side",
        "B": "Angles that add up to 180°",
        "C": "Angles that are opposite each other",
        "D": "Angles that have equal measure"
      },
      "correct_answer": "A"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "If two angles are adjacent, they must:",
      "options": {
        "A": "Have equal measures",
        "B": "Share a common vertex and arm",
        "C": "Always add to 90°",
        "D": "Be acute angles"
      },
      "correct_answer": "B"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "Adjacent angles formed when two lines intersect are:",
      "options": {
        "A": "Always complementary",
        "B": "Always supplementary",
        "C": "Always equal",
        "D": "Always right angles"
      },
      "correct_answer": "B"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "Which pair represents adjacent angles?",
      "options": {
        "A": "Angles sharing vertex O and arm OB",
        "B": "Vertically opposite angles",
        "C": "Angles on opposite sides of transversal",
        "D": "Alternate interior angles"
      },
      "correct_answer": "A"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "Adjacent angles on a straight line sum to:",
      "options": {
        "A": "90°",
        "B": "180°",
        "C": "360°",
        "D": "270°"
      },
      "correct_answer": "B"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "If two adjacent angles are equal, each could measure:",
      "options": {
        "A": "45°",
        "B": "90°",
        "C": "60°",
        "D": "Any of these depending on situation"
      },
      "correct_answer": "D"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "Adjacent angles that are complementary sum to:",
      "options": {
        "A": "90°",
        "B": "180°",
        "C": "360°",
        "D": "45°"
      },
      "correct_answer": "A"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "In the figure with ∠AOB and ∠BOC adjacent, they share:",
      "options": {
        "A": "Vertex O and arm OB",
        "B": "Vertex B and arm OA",
        "C": "Vertex A and arm OC",
        "D": "Only vertex O"
      },
      "correct_answer": "A"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "Adjacent angles that form a straight line are called:",
      "options": {
        "A": "Linear pair",
        "B": "Vertically opposite angles",
        "C": "Complementary angles",
        "D": "Supplementary angles"
      },
      "correct_answer": "A"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "If two adjacent angles are supplementary, their non-common arms form:",
      "options": {
        "A": "A straight line",
        "B": "A right angle",
        "C": "An acute angle",
        "D": "Parallel lines"
      },
      "correct_answer": "A"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "Which is always true for adjacent angles?",
      "options": {
        "A": "They share a common vertex and arm",
        "B": "They are equal",
        "C": "They are acute",
        "D": "They are obtuse"
      },
      "correct_answer": "A"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "If ∠A = 40° and ∠B = 50° are adjacent, they are:",
      "options": {
        "A": "Complementary",
        "B": "Supplementary",
        "C": "Equal",
        "D": "Linear pair"
      },
      "correct_answer": "A"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "Adjacent angles can be:",
      "options": {
        "A": "Both acute",
        "B": "Both obtuse",
        "C": "One acute and one obtuse",
        "D": "All of these"
      },
      "correct_answer": "D"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "The sum of adjacent angles around a point is:",
      "options": {
        "A": "360°",
        "B": "180°",
        "C": "90°",
        "D": "270°"
      },
      "correct_answer": "A"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "If two adjacent angles form a linear pair, they are always:",
      "options": {
        "A": "Supplementary",
        "B": "Complementary",
        "C": "Equal",
        "D": "Right angles"
      },
      "correct_answer": "A"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "Adjacent angles that are not supplementary:",
      "options": {
        "A": "Can still share vertex and arm",
        "B": "Must be complementary",
        "C": "Must be equal",
        "D": "Cannot exist"
      },
      "correct_answer": "A"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "When a right angle is bisected, the two adjacent angles formed are each:",
      "options": {
        "A": "45°",
        "B": "90°",
        "C": "180°",
        "D": "60°"
      },
      "correct_answer": "A"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "Two adjacent angles are in ratio 2:3 and form a linear pair. The angles are:",
      "options": {
        "A": "72° and 108°",
        "B": "60° and 90°",
        "C": "40° and 60°",
        "D": "80° and 120°"
      },
      "correct_answer": "A"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "If adjacent angles are complementary, each angle is:",
      "options": {
        "A": "Less than 90°",
        "B": "Exactly 90°",
        "C": "More than 90°",
        "D": "Either less or more than 90°"
      },
      "correct_answer": "A"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "Adjacent angles formed by perpendicular lines are each:",
      "options": {
        "A": "90°",
        "B": "45°",
        "C": "180°",
        "D": "60°"
      },
      "correct_answer": "A"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "Two adjacent angles are in ratio 4:5 and form a linear pair. The smaller angle is:",
      "options": {
        "A": "80°",
        "B": "100°",
        "C": "60°",
        "D": "120°"
      },
      "correct_answer": "A"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "Adjacent angles on a straight line are always supplementary. This is:",
      "options": {
        "A": "Always true",
        "B": "Sometimes true",
        "C": "Never true",
        "D": "True only for right angles"
      },
      "correct_answer": "A"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "If adjacent angles are (2x+30)° and (3x-10)° and form a linear pair, x equals:",
      "options": {
        "A": "32",
        "B": "28",
        "C": "36",
        "D": "40"
      },
      "correct_answer": "A"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "Two adjacent angles differ by 20° and form a linear pair. The angles are:",
      "options": {
        "A": "80° and 100°",
        "B": "70° and 90°",
        "C": "60° and 80°",
        "D": "50° and 70°"
      },
      "correct_answer": "A"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "In a triangle, two adjacent interior angles:",
      "options": {
        "A": "Share a side of the triangle",
        "B": "Are always complementary",
        "C": "Are always supplementary",
        "D": "Are always equal"
      },
      "correct_answer": "A"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "Adjacent angles at a point on one side of a line sum to:",
      "options": {
        "A": "180°",
        "B": "90°",
        "C": "360°",
        "D": "270°"
      },
      "correct_answer": "A"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "When two lines intersect, how many pairs of adjacent angles are formed?",
      "options": {
        "A": "4",
        "B": "2",
        "C": "6",
        "D": "8"
      },
      "correct_answer": "A"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "Adjacent angles that are complementary and equal are each:",
      "options": {
        "A": "45°",
        "B": "90°",
        "C": "60°",
        "D": "30°"
      },
      "correct_answer": "A"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "In a parallelogram, adjacent angles are:",
      "options": {
        "A": "Supplementary",
        "B": "Complementary",
        "C": "Equal",
        "D": "Right angles"
      },
      "correct_answer": "A"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "If adjacent angles are (x+25)° and (2x-5)° and are complementary, x equals:",
      "options": {
        "A": "20",
        "B": "25",
        "C": "30",
        "D": "35"
      },
      "correct_answer": "B"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "Two adjacent angles of a quadrilateral measure 85° and 95°. They are:",
      "options": {
        "A": "Supplementary",
        "B": "Complementary",
        "C": "Equal",
        "D": "None of these"
      },
      "correct_answer": "A"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "Adjacent angles in a rhombus are:",
      "options": {
        "A": "Supplementary",
        "B": "Complementary",
        "C": "Equal",
        "D": "Right angles"
      },
      "correct_answer": "A"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "If adjacent angles are (3x)° and (7x)° and form a linear pair, the larger angle is:",
      "options": {
        "A": "126°",
        "B": "54°",
        "C": "108°",
        "D": "72°"
      },
      "correct_answer": "A"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "In a rectangle, adjacent angles are:",
      "options": {
        "A": "Right angles",
        "B": "Supplementary",
        "C": "Equal",
        "D": "All of these"
      },
      "correct_answer": "D"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "Adjacent angles formed when two parallel lines are cut by a transversal are:",
      "options": {
        "A": "Supplementary",
        "B": "Complementary",
        "C": "Equal",
        "D": "Right angles"
      },
      "correct_answer": "A"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "If two adjacent angles are supplementary and one is 4 times the other, the smaller angle is:",
      "options": {
        "A": "36°",
        "B": "144°",
        "C": "72°",
        "D": "108°"
      },
      "correct_answer": "A"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "In a cyclic quadrilateral, opposite angles are supplementary. Adjacent angles:",
      "options": {
        "A": "Are not necessarily supplementary",
        "B": "Are always supplementary",
        "C": "Are always complementary",
        "D": "Are always equal"
      },
      "correct_answer": "A"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "If adjacent angles are (5x-20)° and (2x+10)° and are equal, x equals:",
      "options": {
        "A": "10",
        "B": "15",
        "C": "20",
        "D": "25"
      },
      "correct_answer": "A"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "Adjacent interior angles of a polygon share:",
      "options": {
        "A": "A common side",
        "B": "A common vertex",
        "C": "Both a common side and vertex",
        "D": "Neither a common side nor vertex"
      },
      "correct_answer": "C"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "Two adjacent angles measure 110° and 70°. Their relationship is:",
      "options": {
        "A": "Supplementary",
        "B": "Complementary",
        "C": "Equal",
        "D": "None of these"
      },
      "correct_answer": "A"
    },
    {
      "id": 41,
      "difficulty": "hard",
      "question": "In triangle ABC, altitude AD from A meets BC at D. ∠BAD and ∠CAD are adjacent angles that:",
      "options": {
        "A": "Share vertex A and arm AD",
        "B": "Are complementary",
        "C": "Are supplementary",
        "D": "Are equal"
      },
      "correct_answer": "A"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "Two adjacent angles are in ratio 7:8 and their difference is 10°. The angles are:",
      "options": {
        "A": "70° and 80°",
        "B": "60° and 70°",
        "C": "80° and 90°",
        "D": "90° and 100°"
      },
      "correct_answer": "A"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "In a regular pentagon, each interior angle is 108°. Adjacent interior angles:",
      "options": {
        "A": "Are not supplementary",
        "B": "Are supplementary",
        "C": "Are complementary",
        "D": "Are equal"
      },
      "correct_answer": "A"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "If adjacent angles (3x+10)° and (2x+20)° form a linear pair, and a line bisects the larger angle, each bisected part measures:",
      "options": {
        "A": "55°",
        "B": "65°",
        "C": "70°",
        "D": "80°"
      },
      "correct_answer": "B"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "In a triangle, an exterior angle and its adjacent interior angle are:",
      "options": {
        "A": "Supplementary",
        "B": "Complementary",
        "C": "Equal",
        "D": "Right angles"
      },
      "correct_answer": "A"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "If adjacent angles satisfy 2∠A = 3∠B and they are complementary, ∠A measures:",
      "options": {
        "A": "54°",
        "B": "36°",
        "C": "60°",
        "D": "30°"
      },
      "correct_answer": "A"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "In a quadrilateral, three adjacent angles measure 85°, 95°, and 110°. The fourth angle is:",
      "options": {
        "A": "70°",
        "B": "80°",
        "C": "90°",
        "D": "100°"
      },
      "correct_answer": "A"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "Two lines intersect forming four angles. If one adjacent pair is in ratio 2:3, the other adjacent pair is in ratio:",
      "options": {
        "A": "2:3",
        "B": "3:2",
        "C": "1:1",
        "D": "Cannot be determined"
      },
      "correct_answer": "B"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "If adjacent supplementary angles have perpendicular bisectors, the angles are:",
      "options": {
        "A": "90° each",
        "B": "60° and 120°",
        "C": "45° and 135°",
        "D": "30° and 150°"
      },
      "correct_answer": "A"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "In a hexagon, adjacent interior angles differ by 20°. If the smallest is 100°, the largest adjacent to it is:",
      "options": {
        "A": "120°",
        "B": "140°",
        "C": "160°",
        "D": "180°"
      },
      "correct_answer": "B"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "If adjacent angles are (5x-5)° and (4x+5)° and form a linear pair, their difference is:",
      "options": {
        "A": "20°",
        "B": "25°",
        "C": "30°",
        "D": "35°"
      },
      "correct_answer": "A"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "In triangle ABC, ∠A and ∠B are adjacent with respect to side AB. If ∠A=60° and ∠B=80°, then ∠C is:",
      "options": {
        "A": "40°",
        "B": "50°",
        "C": "60°",
        "D": "70°"
      },
      "correct_answer": "A"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "The property that adjacent angles in a parallelogram are supplementary helps prove that:",
      "options": {
        "A": "Opposite sides are parallel",
        "B": "Diagonals bisect each other",
        "C": "Opposite angles are equal",
        "D": "All sides are equal"
      },
      "correct_answer": "A"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "If adjacent angles of a quadrilateral are (x+10)°, (x+20)°, (x+30)°, and (x+40)°, their sum is:",
      "options": {
        "A": "360°",
        "B": "340°",
        "C": "350°",
        "D": "330°"
      },
      "correct_answer": "A"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "Two adjacent angles satisfy: twice one plus three times the other equals 320°. If they are supplementary, the angles are:",
      "options": {
        "A": "80° and 100°",
        "B": "70° and 110°",
        "C": "60° and 120°",
        "D": "50° and 130°"
      },
      "correct_answer": "B"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "In a polygon, if each adjacent pair of interior angles differs by 10°, and there are n sides, which equation is correct?",
      "options": {
        "A": "(n-2)×180 = sum of angles",
        "B": "n/2 × [2a + (n-1)×10] = (n-2)×180",
        "C": "Both A and B",
        "D": "Neither A nor B"
      },
      "correct_answer": "C"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "If bisectors of two adjacent supplementary angles are perpendicular, each original angle is:",
      "options": {
        "A": "90°",
        "B": "60°",
        "C": "120°",
        "D": "135°"
      },
      "correct_answer": "A"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "In a triangle, angle bisector divides opposite side in ratio of adjacent sides. The 'adjacent angles' refer to:",
      "options": {
        "A": "Angles at the vertex",
        "B": "Supplementary angles",
        "C": "Complementary angles",
        "D": "Equal angles"
      },
      "correct_answer": "A"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "Two adjacent angles of a parallelogram are (2x-30)° and (x+60)°. The value of x is:",
      "options": {
        "A": "50",
        "B": "60",
        "C": "70",
        "D": "80"
      },
      "correct_answer": "A"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "Three lines intersect at one point forming six angles. Five angles are 40°, 60°, 80°, 100°, 120°. The sixth angle is:",
      "options": {
        "A": "140°",
        "B": "160°",
        "C": "180°",
        "D": "200°"
      },
      "correct_answer": "A"
    }
  ]
}