{
  "title": "Congruent Angles - Grade 7 CBSE",
  "total_questions": 150,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What does it mean for two angles to be congruent?", "options": {"A": "They add to 90°", "B": "They have equal measures", "C": "They add to 180°", "D": "They are adjacent"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "If ∠A = 45° and ∠B = 45°, then ∠A and ∠B are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "Vertical"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "Which symbol represents angle congruence?", "options": {"A": "=", "B": "≈", "C": "≅", "D": "∼"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "If two angles are congruent, they have:", "options": {"A": "Same vertex", "B": "Same arms", "C": "Same measure", "D": "Same position"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "Vertical angles are always:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "Adjacent"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "If ∠P ≅ ∠Q, and ∠P = 60°, then ∠Q =", "options": {"A": "30°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "All right angles are:", "options": {"A": "Acute", "B": "Obtuse", "C": "Congruent", "D": "Supplementary"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "If two lines intersect, the opposite angles are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "Equal to 90°"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "Corresponding angles formed by parallel lines and a transversal are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "None of these"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "If ∠A ≅ ∠B and ∠B ≅ ∠C, then:", "options": {"A": "∠A ≅ ∠C", "B": "∠A + ∠C = 180°", "C": "∠A and ∠C are complementary", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Alternate interior angles are congruent when lines are:", "options": {"A": "Intersecting", "B": "Parallel", "C": "Perpendicular", "D": "Coincident"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "If two angles are congruent, they can have:", "options": {"A": "Different measures", "B": "Same measure but different positions", "C": "Same vertex only", "D": "Same arms only"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "Base angles of an isosceles triangle are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "Right angles"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "If ∠X = 75° and ∠Y = 75°, we write:", "options": {"A": "∠X = ∠Y", "B": "∠X ≅ ∠Y", "C": "Both A and B", "D": "∠X ≈ ∠Y"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "Angles opposite equal sides in a triangle are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "Right angles"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "All straight angles are:", "options": {"A": "Acute", "B": "Congruent", "C": "Right angles", "D": "Obtuse"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "If two angles are congruent, their supplements are:", "options": {"A": "Equal", "B": "Complementary", "C": "Supplementary", "D": "None of these"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "In a rectangle, all angles are:", "options": {"A": "Acute", "B": "Obtuse", "C": "Right and congruent", "D": "Different"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "If ∠A and ∠B are vertical angles and ∠A = 40°, then ∠B =", "options": {"A": "40°", "B": "50°", "C": "140°", "D": "90°"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Congruent angles can be:", "options": {"A": "Only acute", "B": "Only obtuse", "C": "Only right", "D": "Any type"}, "correct_answer": "D"},
    
    {"id": 21, "difficulty": "medium", "question": "If ∠P = (2x+10)° and ∠Q = (3x-20)° are congruent, find x.", "options": {"A": "10", "B": "20", "C": "30", "D": "40"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "In isosceles triangle ABC with AB = AC, if ∠B = 65°, find ∠C.", "options": {"A": "25°", "B": "50°", "C": "65°", "D": "115°"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "Two parallel lines are cut by a transversal. If one corresponding angle is 110°, find its alternate interior angle.", "options": {"A": "70°", "B": "110°", "C": "120°", "D": "180°"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "If ∠A ≅ ∠B and ∠A is complement of 40°, find ∠B.", "options": {"A": "40°", "B": "50°", "C": "90°", "D": "140°"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "In parallelogram ABCD, opposite angles are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "Equal to 90°"}, "correct_answer": "C"},
   {
  "id": 26,
  "difficulty": "medium",
  "question": "One angle is 3 times its complement. Find the angle.",
  "options": {
    "A": "45°",
    "B": "60°",
    "C": "67.5°",
    "D": "75°"
  },
  "correct_answer": "C"
}
, {"id": 27, "difficulty": "medium", "question": "In rhombus, opposite angles are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "Equal to 60°"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "If ∠X = (5y-10)° and ∠Y = (3y+20)° are vertical angles, find y.", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "In ΔABC ≅ ΔPQR, if ∠A = 55°, find ∠P.", "options": {"A": "35°", "B": "55°", "C": "70°", "D": "125°"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "If two angles are congruent and supplementary, each angle is:", "options": {"A": "30°", "B": "45°", "C": "90°", "D": "120°"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "In isosceles trapezoid, base angles are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "Right angles"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "If ∠M = (4x-5)° and ∠N = (2x+25)° are congruent, find their measure.", "options": {"A": "35°", "B": "55°", "C": "65°", "D": "75°"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "Angles in same segment of a circle are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "Right angles"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "If two angles are congruent and one is 20° more than its supplement, find the angles.", "options": {"A": "80°, 80°", "B": "90°, 90°", "C": "100°, 100°", "D": "110°, 110°"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "In kite, one pair of opposite angles are congruent. Which pair?", "options": {"A": "Angles between unequal sides", "B": "Angles between equal sides", "C": "All angles", "D": "No angles are congruent"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "If ∠A ≅ ∠B and ∠A's complement is 25°, find ∠B.", "options": {"A": "25°", "B": "65°", "C": "90°", "D": "155°"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "In regular pentagon, all interior angles are:", "options": {"A": "60°", "B": "90°", "C": "108° and congruent", "D": "120°"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "If vertical angles are (3x+10)° and (5x-30)°, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "Angles opposite to equal sides in an isosceles triangle are congruent. This is called:", "options": {"A": "Base angle theorem", "B": "Isosceles triangle theorem", "C": "Both A and B", "D": "Pythagorean theorem"}, "correct_answer": "C"},
   {
  "id": 40,
  "difficulty": "medium",
  "question": "If two angles are congruent and one is 15° less than 4 times its complement, find the angles.",
  "options": {
    "A": "49°, 49°",
    "B": "59°, 59°",
    "C": "69°, 69°",
    "D": "79°, 79°"
  },
  "correct_answer": "C"
}
, {"id": 41, "difficulty": "medium", "question": "In cyclic quadrilateral, opposite angles are:", "options": {"A": "Congruent", "B": "Supplementary", "C": "Complementary", "D": "Equal"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "If ∠P = (7x-5)° and ∠Q = (3x+35)° are congruent, find x.", "options": {"A": "5", "B": "8", "C": "10", "D": "12"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "medium", "question": "In equilateral triangle, all angles are:", "options": {"A": "45°", "B": "60° and congruent", "C": "90°", "D": "120°"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "If two angles are congruent and their sum is 140°, find each angle.", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "Angles in alternate segments are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "Equal to 90°"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "If base angles of isosceles triangle are (2x+20)° and (3x-10)°, find x.", "options": {"A": "10", "B": "20", "C": "30", "D": "40"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "In square, all angles are:", "options": {"A": "60°", "B": "90° and congruent", "C": "108°", "D": "120°"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "If ∠A ≅ ∠B and ∠A = 1/3 of right angle, find ∠B.", "options": {"A": "15°", "B": "30°", "C": "45°", "D": "60°"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "Angles subtended by same chord at circumference are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "Right angles"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "If two congruent angles are complementary, each is:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "In regular hexagon, each interior angle is:", "options": {"A": "60°", "B": "90°", "C": "120° and congruent", "D": "135°"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "If vertical angles measure (4x-15)° and (2x+45)°, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "medium", "question": "Angles in corresponding positions with parallel lines are:", "options": {"A": "Supplementary", "B": "Congruent", "C": "Complementary", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "If ∠X ≅ ∠Y and ∠X's supplement is 120°, find ∠Y.", "options": {"A": "30°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "In isosceles right triangle, acute angles are:", "options": {"A": "30°", "B": "45° and congruent", "C": "60°", "D": "90°"}, "correct_answer": "B"},
  {
    "id": 56,
    "difficulty": "medium",
    "question": "If two angles are congruent and one is 20° more than twice its complement, find the angles.",
    "options": {
      "A": "40°, 40°",
      "B": "50°, 50°",
      "C": "66.67°, 66.67°",
      "D": "70°, 70°"
    },
    "correct_answer": "C"
  }
, {"id": 57, "difficulty": "medium", "question": "Angles opposite equal chords are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Congruent", "D": "Right angles"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "If base angles of isosceles triangle are 55° each, find vertex angle.", "options": {"A": "55°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "In regular octagon, each interior angle is:", "options": {"A": "108°", "B": "120°", "C": "135° and congruent", "D": "150°"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "If ∠A = (5x+10)° and ∠B = (7x-20)° are congruent, find their measure.", "options": {"A": "55°", "B": "65°", "C": "75°", "D": "85°"}, "correct_answer": "D"},
    {"id": 61, "difficulty": "medium", "question": "Angles in same segment of circle standing on same arc are:", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "If two angles are congruent and supplementary to 70°, find the angles.", "options": {"A": "70°, 70°", "B": "90°, 90°", "C": "110°, 110°", "D": "120°, 120°"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "In parallelogram, consecutive angles are:", "options": {"A": "Congruent", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "If ∠P ≅ ∠Q and ∠P = 2/3 of straight angle, find ∠Q.", "options": {"A": "60°", "B": "90°", "C": "120°", "D": "150°"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "Angles subtended by diameter are:", "options": {"A": "45°", "B": "90° and congruent", "C": "120°", "D": "180°"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "If two congruent angles add to 100°, find each angle.", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "80°"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "In regular polygon with n sides, each exterior angle is:", "options": {"A": "360/n degrees", "B": "180(n-2)/n degrees", "C": "90°", "D": "60°"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "If vertical angles are (6x-24)° and (4x+36)°, find x.", "options": {"A": "12", "B": "15", "C": "20", "D": "30"}, "correct_answer": "D"},
    {"id": 69, "difficulty": "medium", "question": "Angles in alternate exterior positions with parallel lines are:", "options": {"A": "Supplementary", "B": "Congruent", "C": "Complementary", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "If ∠X ≅ ∠Y and ∠X's complement is 35°, find ∠Y.", "options": {"A": "35°", "B": "55°", "C": "90°", "D": "125°"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "In rhombus, adjacent angles are:", "options": {"A": "Congruent", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "B"},
  {
    "id": 72,
    "difficulty": "medium",
    "question": "If two angles are congruent and one is 20° less than 3 times its complement, find the angles.",
    "options": {
      "A": "40°, 40°",
      "B": "50°, 50°",
      "C": "62.5°, 62.5°",
      "D": "70°, 70°"
    },
    "correct_answer": "C"
  }
,  {"id": 73, "difficulty": "medium", "question": "Angles in same segment but different arcs are:", "options": {"A": "Equal if arcs equal", "B": "Always equal", "C": "Supplementary", "D": "Complementary"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "If base angles of isosceles triangle are 65° each, find vertex angle.", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "In regular decagon, each interior angle is:", "options": {"A": "120°", "B": "135°", "C": "144° and congruent", "D": "150°"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "If ∠A = (3x+15)° and ∠B = (5x-25)° are congruent, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "Angles on same side of transversal with parallel lines are:", "options": {"A": "Congruent", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "If ∠P ≅ ∠Q and ∠P = 1/4 of revolution, find ∠Q.", "options": {"A": "45°", "B": "90°", "C": "135°", "D": "180°"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "In kite, angles between unequal sides are:", "options": {"A": "Congruent", "B": "Supplementary", "C": "Complementary", "D": "Not necessarily equal"}, "correct_answer": "D"},
    {"id": 80, "difficulty": "medium", "question": "If two congruent angles are in ratio 1:1 and sum is 120°, find each angle.", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "C"},
    
  {
  "id": 81,
  "difficulty": "hard",
  "question": "In ΔABC, ∠A = (3x+10)°, ∠B = (2x+20)°, ∠C = (4x-30)°. If ΔABC ≅ ΔPQR and ∠A ≅ ∠P, find x and ∠C.",
  "options": {
    "A": "x=20, ∠C=50°",
    "B": "x=25, ∠C=70°",
    "C": "x=30, ∠C=90°",
    "D": "x=35, ∠C=110°"
  },
  "correct_answer": "A"
}
,  {
  "id": 82,
  "difficulty": "hard",
  "question": "Two parallel lines are cut by a transversal. If one interior angle is (6x - 40)° and its corresponding angle is (4x + 20)°, find the measure of all eight angles.",
  "options": {
    "A": "40°, 140°, 40°, 140°, 40°, 140°, 40°, 140°",
    "B": "50°, 130°, 50°, 130°, 50°, 130°, 50°, 130°",
    "C": "60°, 120°, 60°, 120°, 60°, 120°, 60°, 120°",
    "D": "70°, 110°, 70°, 110°, 70°, 110°, 70°, 110°"
  },
  "correct_answer": "A"
}

,{
  "id": 83,
  "difficulty": "hard",
  "question": "In cyclic quadrilateral ABCD, ∠A = (2x+20)°, ∠B = (3y-10)°, ∠C = (2x+40)°, ∠D = (3y+10)°. Find x and y.",
  "options": {
    "A": "x=30, y=25",
    "B": "x=35, y=20",
    "C": "x=40, y=15",
    "D": "x=45, y=10"
  },
  "correct_answer": "A"
}
,   {
    "id": 84,
    "difficulty": "hard",
    "question": "If angles of triangle are (x+20)°, (2x-10)°, and (3x-30)° and triangle is congruent to another with angles (y+10)°, (2y-20)°, (3y-50)°, find x and y.",
    "options": {
      "A": "x=35, y=40",
      "B": "x=40, y=35",
      "C": "x=33.33, y=40",
      "D": "x=40, y=33.33"
    },
    "correct_answer": "C"
  }
,   {
    "id": 85,
    "difficulty": "hard",
    "question": "In regular polygon, each interior angle is 156°. How many sides does it have?",
    "options": {
      "A": "12",
      "B": "15",
      "C": "18",
      "D": "20"
    },
    "correct_answer": "B"
  },  {"id": 86, "difficulty": "hard", "question": "Two lines intersect forming four angles. If one angle is (2x+10)° and its vertically opposite angle is (3x-20)°, find all four angles.", "options": {"A": "50°, 130°, 50°, 130°", "B": "60°, 120°, 60°, 120°", "C": "70°, 110°, 70°, 110°", "D": "80°, 100°, 80°, 100°"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "In ΔABC ≅ ΔDEF, ∠A = (4x-15)°, ∠D = 65°, ∠B = (3y+25)°, ∠E = 85°. Find x and y.", "options": {"A": "x=20, y=20", "B": "x=25, y=15", "C": "x=30, y=10", "D": "x=35, y=5"}, "correct_answer": "A"},
    {
    "id": 88,
    "difficulty": "hard",
    "question": "If exterior angle of a regular polygon is 24°, how many diagonals does it have?",
    "options": {
      "A": "75",
      "B": "90",
      "C": "105",
      "D": "120"
    },
    "correct_answer": "B"
  }, {"id": 89, "difficulty": "hard", "question": "In parallelogram ABCD, ∠A = (3x+10)°, ∠B = (2y+20)°, ∠C = (4x-5)°, ∠D = (3y-15)°. Find x and y.", "options": {"A": "x=25, y=35", "B": "x=30, y=25", "C": "x=35, y=20", "D": "x=40, y=15"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "If angles of quadrilateral are in ratio 1:2:3:4 and it's congruent to another with angles in ratio 4:3:2:1, find the largest angle.", "options": {"A": "120°", "B": "144°", "C": "160°", "D": "172°"}, "correct_answer": "B"},
    {"id": 91, "difficulty": "hard", "question": "In ΔPQR, ∠P:∠Q:∠R = 3:4:5. If ΔPQR ≅ ΔXYZ and ∠X = 45°, find ∠Y and ∠Z.", "options": {"A": "∠Y=60°, ∠Z=75°", "B": "∠Y=55°, ∠Z=80°", "C": "∠Y=65°, ∠Z=70°", "D": "∠Y=70°, ∠Z=65°"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Two parallel lines are cut by two transversals forming triangle. If angles of triangle are (x+30)°, (2x-20)°, (3x-40)°, find x.", "options": {"A": "30", "B": "35", "C": "40", "D": "45"}, "correct_answer": "B"},
  {
    "id": 93,
    "difficulty": "hard",
    "question": "In a rhombus, diagonals intersect at right angles. If one interior angle is (5x−10)°, find x.",
    "options": {
      "A": "10",
      "B": "15",
      "C": "20",
      "D": "25"
    },
    "correct_answer": "C"
  },{"id": 94, "difficulty": "hard", "question": "If interior angle of regular polygon is 8 times its exterior angle, how many sides?", "options": {"A": "16", "B": "18", "C": "20", "D": "24"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "In ΔABC ≅ ΔLMN, ∠A = (2x+3y)°, ∠L = 75°, ∠B = (3x+2y)°, ∠M = 65°. Find x and y.", "options": {"A": "x=15, y=10", "B": "x=12, y=13", "C": "x=10, y=15", "D": "x=13, y=12"}, "correct_answer": "D"},
    {"id": 96, "difficulty": "hard", "question": "If sum of interior angles of polygon is 1440°, how many sides? Each interior angle is congruent in regular polygon.", "options": {"A": "8", "B": "10", "C": "12", "D": "14"}, "correct_answer": "B"},
  {
    "id": 97,
    "difficulty": "hard",
    "question": "In trapezoid ABCD with AB∥CD, ∠A = (4x+5)°, ∠D = (3x+25)°. If ∠A ≅ ∠B and ∠C ≅ ∠D, find all angles.",
    "options": {
      "A": "90°, 90°, 90°, 90°",
      "B": "85°, 85°, 95°, 95°",
      "C": "90.71°, 90.71°, 89.29°, 89.29°",
      "D": "100°, 100°, 80°, 80°"
    },
    "correct_answer": "C"
  }, {"id": 98, "difficulty": "hard", "question": "If exterior angles of polygon are in ratio 1:2:3:4:5, find smallest interior angle.", "options": {"A": "24°", "B": "36°", "C": "48°", "D": "60°"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "In ΔXYZ ≅ ΔABC, ∠X = (a+b)°, ∠A = 55°, ∠Y = (2a-b)°, ∠B = 65°. Find a and b.", "options": {"A": "a=30, b=25", "B": "a=35, b=20", "C": "a=40, b=15", "D": "a=45, b=10"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "Regular polygon has interior angles each 170°. How many diagonals can be drawn from one vertex?", "options": {"A": "15", "B": "33", "C": "21", "D": "24"}, "correct_answer": "B"}
  ,
  {"id":101,"difficulty":"easy","question":"If two angles measure 35° each, they are called:","options":{"A":"Supplementary","B":"Adjacent","C":"Congruent","D":"Linear"},"correct_answer":"C"},
    {"id":102,"difficulty":"easy","question":"Angles formed at the intersection of two straight lines are always:","options":{"A":"Equal","B":"Congruent in opposite pairs","C":"Right angles","D":"Supplementary only"},"correct_answer":"B"},
    {"id":103,"difficulty":"easy","question":"All angles measuring 90° are:","options":{"A":"Acute","B":"Obtuse","C":"Congruent","D":"Straight"},"correct_answer":"C"},
    {"id":104,"difficulty":"easy","question":"If two angles are congruent, their measures are:","options":{"A":"Unequal","B":"Proportional","C":"Equal","D":"Opposite"},"correct_answer":"C"},
    {"id":105,"difficulty":"easy","question":"Which pair of angles are always congruent?","options":{"A":"Adjacent angles","B":"Vertical angles","C":"Linear pair","D":"Supplementary angles"},"correct_answer":"B"},
    {"id":106,"difficulty":"easy","question":"Angles opposite equal sides of a triangle are:","options":{"A":"Right","B":"Obtuse","C":"Congruent","D":"Complementary"},"correct_answer":"C"},
    {"id":107,"difficulty":"easy","question":"If two angles have same measure but different positions, they are:","options":{"A":"Equal","B":"Congruent","C":"Supplementary","D":"Linear"},"correct_answer":"B"},
    {"id":108,"difficulty":"easy","question":"Alternate interior angles are congruent when lines are:","options":{"A":"Intersecting","B":"Parallel","C":"Perpendicular","D":"Coincident"},"correct_answer":"B"},
    {"id":109,"difficulty":"easy","question":"Angles in a square are:","options":{"A":"Acute","B":"Obtuse","C":"Right and congruent","D":"Different"},"correct_answer":"C"},
    {"id":110,"difficulty":"easy","question":"If ∠A ≅ ∠B and ∠A = 40°, then ∠B =","options":{"A":"20°","B":"40°","C":"80°","D":"140°"},"correct_answer":"B"},
    {"id":111,"difficulty":"easy","question":"All straight angles are:","options":{"A":"90°","B":"Obtuse","C":"Congruent","D":"Acute"},"correct_answer":"C"},
    {"id":112,"difficulty":"easy","question":"Corresponding angles are congruent if lines are cut by a transversal and are:","options":{"A":"Intersecting","B":"Parallel","C":"Skew","D":"Coincident"},"correct_answer":"B"},
    {"id":113,"difficulty":"easy","question":"Angles with equal measures are called:","options":{"A":"Adjacent","B":"Congruent","C":"Linear","D":"Vertical only"},"correct_answer":"B"},
    {"id":114,"difficulty":"easy","question":"In an equilateral triangle, all angles are:","options":{"A":"45°","B":"60° and congruent","C":"90°","D":"120°"},"correct_answer":"B"},
    {"id":115,"difficulty":"easy","question":"Which symbol denotes angle congruence?","options":{"A":"=","B":"≈","C":"≅","D":"∼"},"correct_answer":"C"},
    {"id":116,"difficulty":"easy","question":"If two angles are vertical, they are:","options":{"A":"Supplementary","B":"Complementary","C":"Congruent","D":"Linear"},"correct_answer":"C"},
    {"id":117,"difficulty":"easy","question":"Angles formed by diameter at the circle are:","options":{"A":"Acute","B":"Obtuse","C":"Right and congruent","D":"Straight"},"correct_answer":"C"},
    {"id":118,"difficulty":"easy","question":"If ∠P = ∠Q, then we say ∠P and ∠Q are:","options":{"A":"Adjacent","B":"Linear","C":"Congruent","D":"Supplementary"},"correct_answer":"C"},
    {"id":119,"difficulty":"easy","question":"Angles in a rectangle are always:","options":{"A":"Acute","B":"Obtuse","C":"Right and congruent","D":"Unequal"},"correct_answer":"C"},
    {"id":120,"difficulty":"easy","question":"Congruent angles can be acute, obtuse or right because they depend on:","options":{"A":"Position","B":"Measure","C":"Vertex","D":"Direction"},"correct_answer":"B"},

    {"id":121,"difficulty":"medium","question":"If ∠A = (3x+15)° and ∠B = (5x−25)° are congruent, find x.","options":{"A":"10","B":"15","C":"20","D":"25"},"correct_answer":"C"},
    {"id":122,"difficulty":"medium","question":"Two congruent angles are supplementary. Find each angle.","options":{"A":"45°","B":"60°","C":"90°","D":"120°"},"correct_answer":"C"},
    {"id":123,"difficulty":"medium","question":"In isosceles triangle, base angles are each 50°. Find vertex angle.","options":{"A":"60°","B":"70°","C":"80°","D":"90°"},"correct_answer":"C"},
    {"id":124,"difficulty":"medium","question":"If ∠P ≅ ∠Q and ∠P is complement of 35°, find ∠Q.","options":{"A":"35°","B":"45°","C":"55°","D":"65°"},"correct_answer":"C"},
    {"id":125,"difficulty":"medium","question":"Angles in a regular hexagon are congruent. Find each interior angle.","options":{"A":"90°","B":"100°","C":"120°","D":"135°"},"correct_answer":"C"},
    {"id":126,"difficulty":"medium","question":"If vertical angles are (4x−12)° and (2x+28)°, find x.","options":{"A":"8","B":"10","C":"12","D":"14"},"correct_answer":"C"},
    {"id":127,"difficulty":"medium","question":"Two congruent angles add up to 140°. Find each angle.","options":{"A":"60°","B":"65°","C":"70°","D":"75°"},"correct_answer":"C"},
    {"id":128,"difficulty":"medium","question":"In a parallelogram, which angles are congruent?","options":{"A":"Adjacent","B":"Opposite","C":"All","D":"None"},"correct_answer":"B"},
    {"id":129,"difficulty":"medium","question":"If one angle of a linear pair is congruent to the other, find each angle.","options":{"A":"45°","B":"60°","C":"90°","D":"120°"},"correct_answer":"C"},
    {"id":130,"difficulty":"medium","question":"In a circle, angles subtended by the same chord are:","options":{"A":"Supplementary","B":"Congruent","C":"Complementary","D":"Right"},"correct_answer":"B"},

    {"id":131,"difficulty":"hard","question":"Angles of a triangle are in ratio 2:3:4. If the triangle is congruent to another, find the largest angle.","options":{"A":"60°","B":"72°","C":"80°","D":"90°"},"correct_answer":"C"},
    {"id":132,"difficulty":"hard","question":"In ΔABC ≅ ΔPQR, ∠A = (x+20)°, ∠P = 60°. Find x and ∠B if ∠B = 2x.","options":{"A":"x=40, ∠B=80°","B":"x=30, ∠B=60°","C":"x=20, ∠B=40°","D":"x=50, ∠B=100°"},"correct_answer":"B"},
    {"id":133,"difficulty":"hard","question":"Exterior angle of a regular polygon is 30°. How many sides does it have?","options":{"A":"10","B":"12","C":"15","D":"18"},"correct_answer":"B"},
    {"id":134,"difficulty":"hard","question":"Two congruent angles form a linear pair. Find each angle.","options":{"A":"60°","B":"75°","C":"90°","D":"120°"},"correct_answer":"C"},
    {"id":135,"difficulty":"hard","question":"In cyclic quadrilateral, one angle is 70°. Find its opposite angle.","options":{"A":"70°","B":"90°","C":"110°","D":"140°"},"correct_answer":"C"},
    {"id":136,"difficulty":"hard","question":"If angles of quadrilateral are congruent, find each angle.","options":{"A":"60°","B":"75°","C":"90°","D":"120°"},"correct_answer":"C"},
    {"id":137,"difficulty":"hard","question":"Two congruent angles are each 15° more than their complement. Find the angles.","options":{"A":"45°","B":"50°","C":"55°","D":"60°"},"correct_answer":"C"},
    {"id":138,"difficulty":"hard","question":"Interior angle of regular polygon is 150°. Find number of sides.","options":{"A":"10","B":"12","C":"15","D":"18"},"correct_answer":"B"},
    {"id":139,"difficulty":"hard","question":"In ΔABC ≅ ΔXYZ, ∠A = 3x, ∠X = 60°. Find x and ∠B if ∠B = x+20.","options":{"A":"x=20, ∠B=40°","B":"x=15, ∠B=35°","C":"x=25, ∠B=45°","D":"x=30, ∠B=50°"},"correct_answer":"A"},
    {"id":140,"difficulty":"hard","question":"Angles of a regular polygon are congruent and sum to 2160°. How many sides?","options":{"A":"10","B":"12","C":"14","D":"16"},"correct_answer":"B"},
    {"id":141,"difficulty":"hard","question":"Two congruent right angles form a straight line. What is their sum?","options":{"A":"90°","B":"120°","C":"150°","D":"180°"},"correct_answer":"D"},
    {"id":142,"difficulty":"hard","question":"If exterior angle of regular polygon is equal to each interior angle divided by 5, find number of sides.","options":{"A":"6","B":"8","C":"10","D":"12"},"correct_answer":"C"},
    {"id":143,"difficulty":"hard","question":"In triangle, angles are (x+10)°, (2x+20)°, (3x−30)°. Triangle is congruent to another. Find largest angle.","options":{"A":"70°","B":"80°","C":"90°","D":"100°"},"correct_answer":"C"},
    {"id":144,"difficulty":"hard","question":"Angles in ratio 1:1:2 form a triangle congruent to another. Find smallest angle.","options":{"A":"30°","B":"45°","C":"60°","D":"75°"},"correct_answer":"A"},
    {"id":145,"difficulty":"hard","question":"In regular polygon, number of sides equals number of congruent interior angles. If each interior angle is 135°, find sides.","options":{"A":"6","B":"8","C":"10","D":"12"},"correct_answer":"B"},
    {"id":146,"difficulty":"hard","question":"Two congruent triangles have one angle 40° and another 70°. Find third angle.","options":{"A":"60°","B":"70°","C":"80°","D":"90°"},"correct_answer":"C"},
  {
    "id": 147,
    "difficulty": "hard",
    "question": "If each interior angle of a regular polygon is congruent and equals 160°, how many sides?",
    "options": {
      "A": "9",
      "B": "12",
      "C": "15",
      "D": "18"
    },
    "correct_answer": "D"
  }, {
  "id": 148,
  "difficulty": "hard",
  "question": "Angles of triangle are congruent to angles of another triangle. If one angle is 58°, find all angles.",
  "options": {
    "A": "58°, 58°, 64°",
    "B": "58°, 58°, 58°",
    "C": "58°, 62°, 60°",
    "D": "58°, 61°, 61°"
  },
  "correct_answer": "C"
}
,{
  "id": 149,
  "difficulty": "hard",
  "question": "Two congruent angles are each 30° less than their supplement. Find the angles.",
  "options": {
    "A": "60°",
    "B": "70°",
    "C": "75°",
    "D": "80°"
  },
  "correct_answer": "C"
}
,   {
    "id": 150,
    "difficulty": "hard",
    "question": "Interior angle of regular polygon is 165°. Find number of diagonals from one vertex.",
    "options": {
      "A": "18",
      "B": "19",
      "C": "20",
      "D": "21"
    },
    "correct_answer": "D"
  }
]
}