{
  "title": "Adjacent and Vertical Angles - Grade 7 CBSE",
  "total_questions": 150,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Two angles that share a common vertex and side but do not overlap are called:", "options": {"A": "Vertical angles", "B": "Adjacent angles", "C": "Supplementary angles", "D": "Complementary angles"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "Vertical angles are always:", "options": {"A": "Adjacent", "B": "Equal", "C": "Supplementary", "D": "Complementary"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "If two lines intersect, how many pairs of vertical angles are formed?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Adjacent angles on a straight line add up to:", "options": {"A": "90°", "B": "180°", "C": "360°", "D": "270°"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "If angle A and angle B are vertical angles, and angle A = 45°, what is angle B?", "options": {"A": "45°", "B": "135°", "C": "90°", "D": "180°"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Two adjacent angles whose measures add up to 90° are called:", "options": {"A": "Vertical angles", "B": "Adjacent complementary angles", "C": "Adjacent supplementary angles", "D": "Linear pair"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Can vertical angles be adjacent to each other?", "options": {"A": "Always", "B": "Sometimes", "C": "Never", "D": "Only when they are right angles"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "If two adjacent angles are 60° and 120°, what is their relationship?", "options": {"A": "They are complementary", "B": "They form a linear pair", "C": "They are vertical angles", "D": "They are equal"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "In the figure, if ∠1 = 70° and it's vertical to ∠2, what is ∠2?", "options": {"A": "110°", "B": "70°", "C": "20°", "D": "290°"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Two angles that are opposite each other when two lines intersect are called:", "options": {"A": "Adjacent angles", "B": "Vertical angles", "C": "Supplementary angles", "D": "Complementary angles"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "If ∠P and ∠Q are adjacent and ∠P = 30°, ∠Q = 60°, what is their sum?", "options": {"A": "30°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "Adjacent angles must share:", "options": {"A": "Only a common vertex", "B": "Only a common side", "C": "Both a common vertex and side", "D": "Neither vertex nor side"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "If two lines intersect at right angles, what are the measures of the vertical angles?", "options": {"A": "45° each", "B": "90° each", "C": "180° each", "D": "60° each"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Can two acute angles be vertical angles?", "options": {"A": "Yes, always", "B": "Yes, sometimes", "C": "No, never", "D": "Only if they are 30° each"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If ∠A and ∠B are vertical angles, and ∠A = 110°, what type of angle is ∠B?", "options": {"A": "Acute angle", "B": "Right angle", "C": "Obtuse angle", "D": "Straight angle"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "Two adjacent angles that form a straight line are called:", "options": {"A": "Vertical angles", "B": "A linear pair", "C": "Complementary angles", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "If ∠X and ∠Y are vertical angles, which statement is always true?", "options": {"A": "∠X + ∠Y = 90°", "B": "∠X + ∠Y = 180°", "C": "∠X = ∠Y", "D": "∠X and ∠Y are adjacent"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "How many degrees are in a complete circle?", "options": {"A": "90°", "B": "180°", "C": "270°", "D": "360°"}, "correct_answer": "D"},
    {"id": 19, "difficulty": "easy", "question": "If two adjacent angles are equal and form a linear pair, each angle measures:", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "180°"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Which of these pairs of angles are always equal?", "options": {"A": "Adjacent angles", "B": "Vertical angles", "C": "Angles in a linear pair", "D": "Complementary angles"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "Two lines intersect forming four angles. If one angle is 75°, what are the measures of the other three angles?", "options": {"A": "75°, 105°, 105°", "B": "75°, 75°, 105°", "C": "75°, 105°, 75°", "D": "105°, 105°, 105°"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "In the figure, ∠A and ∠B are vertical angles. If ∠A = (3x + 10)° and ∠B = (5x - 20)°, find the value of x.", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "C"},
    {
  "id": 23,
  "difficulty": "medium",
  "question": "∠P and ∠Q are adjacent complementary angles. If ∠P = (2x + 5)° and ∠Q = (3x - 25)°, find ∠P.",
  "options": {
    "A": "25°",
    "B": "35°",
    "C": "45°",
    "D": "55°"
  },
  "correct_answer": "C"
}
, {"id": 24, "difficulty": "medium", "question": "If two adjacent angles are (2x + 30)° and (3x - 10)° and they form a linear pair, find the larger angle.", "options": {"A": "70°", "B": "98°", "C": "110°", "D": "82°"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "In the figure, lines AB and CD intersect at O. If ∠AOC = 50°, find ∠BOD.", "options": {"A": "50°", "B": "130°", "C": "40°", "D": "140°"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Two lines intersect. If one of the angles formed is 47°, what is the measure of its adjacent angle?", "options": {"A": "47°", "B": "133°", "C": "43°", "D": "90°"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "∠A and ∠B are vertical angles. If ∠A is 15° more than half of ∠B, find ∠A.", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Three lines intersect at a point forming six angles. If one angle is 40°, how many other angles will have the same measure?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "If two adjacent angles are in the ratio 4:5 and form a linear pair, find the smaller angle.", "options": {"A": "60°", "B": "80°", "C": "100°", "D": "120°"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "In the figure, ∠1 and ∠2 are vertical angles. If ∠1 = (4x - 15)° and ∠2 = (2x + 25)°, find the measure of ∠1.", "options": {"A": "35°", "B": "65°", "C": "85°", "D": "95°"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Two lines intersect. If the sum of two adjacent angles is 150°, what is the measure of the smaller angle?", "options": {"A": "30°", "B": "60°", "C": "75°", "D": "90°"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "∠X and ∠Y are vertical angles. If ∠X = (7y - 12)° and ∠Y = (3y + 28)°, find the value of y.", "options": {"A": "5", "B": "8", "C": "10", "D": "12"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "If an angle measures 125°, what is the measure of its vertical angle?", "options": {"A": "55°", "B": "125°", "C": "35°", "D": "65°"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Two adjacent angles are such that one is 20° more than the other. If they form a linear pair, find the larger angle.", "options": {"A": "80°", "B": "100°", "C": "120°", "D": "140°"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "In the figure, lines PQ and RS intersect at T. If ∠PTR = 70°, find ∠QTS.", "options": {"A": "70°", "B": "110°", "C": "20°", "D": "160°"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "If two vertical angles are (5x + 5)° and (6x - 10)°, find x.", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "∠A and ∠B are adjacent and complementary. If ∠A = 2∠B, find ∠A.", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "Two lines intersect forming an angle of 85°. What is the measure of the angle vertically opposite to it?", "options": {"A": "85°", "B": "95°", "C": "105°", "D": "5°"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "If two adjacent angles are (x + 25)° and (2x - 10)° and their sum is 180°, find x.", "options": {"A": "35", "B": "45", "C": "55", "D": "65"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "∠P and ∠Q are vertical angles. If ∠P = 3∠Q and ∠Q is acute, find ∠P.", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "In a linear pair, if one angle is 35° more than twice the other, find the smaller angle.", "options": {"A": "35°", "B": "45°", "C": "55°", "D": "65°"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "Two lines intersect. If one of the angles formed is 110°, what is the sum of all four angles formed?", "options": {"A": "220°", "B": "360°", "C": "440°", "D": "720°"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "∠M and ∠N are vertical angles. If ∠M = (4a + 8)° and ∠N = (6a - 22)°, find the measure of ∠M.", "options": {"A": "40°", "B": "52°", "C": "68°", "D": "80°"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "If two adjacent angles are supplementary and one is 45°, what is the other?", "options": {"A": "45°", "B": "90°", "C": "135°", "D": "180°"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "In the figure, ∠AOB and ∠BOC are adjacent angles. If ∠AOB = 65° and ∠BOC = 115°, what is their relationship?", "options": {"A": "They are complementary", "B": "They form a linear pair", "C": "They are vertical angles", "D": "They are equal"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "medium", "question": "Two lines intersect at right angles. What is the measure of each vertical angle?", "options": {"A": "45°", "B": "90°", "C": "180°", "D": "360°"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "If ∠X and ∠Y are vertical angles and ∠X = (2y + 30)° and ∠Y = (4y - 20)°, find y.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "In a linear pair, the angles are always:", "options": {"A": "Equal", "B": "Complementary", "C": "Supplementary", "D": "Vertical"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "If two adjacent angles are (3x + 10)° and (2x - 5)° and they are complementary, find x.", "options": {"A": "15", "B": "17", "C": "19", "D": "21"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "∠A and ∠B are vertical angles. If ∠A = 72°, what is the measure of the angle adjacent to ∠B?", "options": {"A": "72°", "B": "108°", "C": "18°", "D": "288°"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Two lines intersect. If three of the angles formed are 70°, 110°, and 70°, what is the fourth angle?", "options": {"A": "70°", "B": "90°", "C": "110°", "D": "130°"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "If ∠P and ∠Q are adjacent and ∠P = 55°, and ∠P + ∠Q = 145°, what is ∠Q?", "options": {"A": "55°", "B": "90°", "C": "125°", "D": "145°"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "Vertical angles are formed when:", "options": {"A": "Two lines are parallel", "B": "Two lines intersect", "C": "Two lines are perpendicular", "D": "A line crosses two parallel lines"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "If two vertical angles are (x + 40)° and (2x - 20)°, find x.", "options": {"A": "20", "B": "40", "C": "60", "D": "80"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "∠A and ∠B form a linear pair. If ∠A = 5∠B, find ∠B.", "options": {"A": "15°", "B": "30°", "C": "45°", "D": "60°"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "In the figure, ∠1 and ∠2 are adjacent angles on a straight line. If ∠1 = 75°, find ∠2.", "options": {"A": "15°", "B": "75°", "C": "105°", "D": "180°"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "If two lines intersect and one angle is 48°, what is the measure of its vertically opposite angle?", "options": {"A": "42°", "B": "48°", "C": "132°", "D": "312°"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "medium", "question": "Two adjacent angles are in the ratio 3:2. If they form a linear pair, find the larger angle.", "options": {"A": "72°", "B": "108°", "C": "120°", "D": "144°"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "∠X and ∠Y are vertical angles. If ∠X = 85°, what is the measure of the angle supplementary to ∠Y?", "options": {"A": "85°", "B": "95°", "C": "105°", "D": "175°"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "If ∠A and ∠B are adjacent complementary angles with ∠A = 25°, what is ∠B?", "options": {"A": "25°", "B": "65°", "C": "155°", "D": "205°"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "Two lines intersect. If one angle is 62°, what is the measure of the angle adjacent to it?", "options": {"A": "28°", "B": "62°", "C": "118°", "D": "152°"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "If vertical angles are (3x - 15)° and (x + 45)°, find the measure of each angle.", "options": {"A": "45°", "B": "60°", "C": "75°", "D": "90°"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "∠P, ∠Q, and ∠R are three angles at a point on a straight line. If ∠P = 50° and ∠Q = 70°, find ∠R.", "options": {"A": "60°", "B": "120°", "C": "180°", "D": "240°"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "If two adjacent angles are supplementary and one is 3 times the other, find the smaller angle.", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "In the figure, lines LM and NO intersect at P. If ∠LPN = 40°, find ∠MPO.", "options": {"A": "40°", "B": "50°", "C": "140°", "D": "180°"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "If ∠A and ∠B are vertical angles and ∠A = 115°, what type of angle is ∠B?", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Straight"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "Two lines intersect forming angles of 55°, 125°, 55°, and x°. Find x.", "options": {"A": "55°", "B": "125°", "C": "180°", "D": "305°"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "∠X and ∠Y are adjacent angles. If ∠X = 35° and ∠X + ∠Y = 180°, what is ∠Y?", "options": {"A": "35°", "B": "55°", "C": "145°", "D": "180°"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "If two vertical angles are (2x + 30)° and (4x - 10)°, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "In a linear pair, if one angle is 20° less than the other, find the larger angle.", "options": {"A": "80°", "B": "100°", "C": "120°", "D": "160°"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "Two lines intersect at point O. If ∠AOC = 75°, find ∠BOD where AOB and COD are straight lines.", "options": {"A": "75°", "B": "105°", "C": "15°", "D": "285°"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "If ∠M and ∠N are vertical angles with ∠M = (5x - 20)° and ∠N = (3x + 40)°, find the measure of ∠M.", "options": {"A": "60°", "B": "80°", "C": "100°", "D": "120°"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "Two adjacent angles are complementary. If one is 40°, what is the other?", "options": {"A": "40°", "B": "50°", "C": "140°", "D": "180°"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "If two lines intersect and one angle is 85°, what is the sum of its adjacent angles?", "options": {"A": "85°", "B": "95°", "C": "175°", "D": "265°"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "∠P and ∠Q form a linear pair. If ∠P = 2∠Q + 30°, find ∠Q.", "options": {"A": "30°", "B": "50°", "C": "70°", "D": "110°"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "Vertical angles are always:", "options": {"A": "Acute", "B": "Equal", "C": "Supplementary", "D": "Adjacent"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "If two adjacent angles are (x + 15)° and (2x - 30)° and they are supplementary, find x.", "options": {"A": "55", "B": "60", "C": "65", "D": "70"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "In the figure, ∠1 and ∠3 are vertical angles. If ∠1 = 65°, what is ∠3?", "options": {"A": "25°", "B": "65°", "C": "115°", "D": "295°"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "Two lines intersect. If one angle is 47°, what is the measure of the angle vertically opposite to it?", "options": {"A": "43°", "B": "47°", "C": "133°", "D": "227°"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "If ∠A and ∠B are adjacent and ∠A = 70°, and they form a linear pair, what is ∠B?", "options": {"A": "20°", "B": "70°", "C": "110°", "D": "290°"}, "correct_answer": "C"},

    {"id": 81, "difficulty": "hard", "question": "In the figure, lines AB, CD, and EF intersect at O. If ∠AOC = 50°, ∠COE = 70°, and AB is a straight line, find ∠DOF.", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "Three lines intersect at a point forming six angles. If the sum of two adjacent angles is 150° and one of the vertical angles is 40°, find all six angles.", "options": {"A": "40°, 40°, 110°, 110°, 70°, 70°", "B": "40°, 40°, 140°, 140°, 70°, 70°", "C": "40°, 40°, 110°, 110°, 30°, 30°", "D": "40°, 140°, 40°, 140°, 100°, 100°"}, "correct_answer": "A"},
   {
  "id": 83,
  "difficulty": "hard",
  "question": "If ∠A and ∠B are vertical angles, and ∠C is adjacent to both. If ∠A = (x + 90)° and ∠C = (90 - x)°, find ∠B.",
  "options": {
    "A": "40°",
    "B": "65°",
    "C": "115°",
    "D": "140°"
  },
  "correct_answer": "C"
}
, {"id": 84, "difficulty": "hard", "question": "Lines PQ and RS intersect at T. Another line TU is drawn such that ∠PTU = 40°. If ∠QTR and ∠STR are vertical angles, and ∠QTR = 2∠STR, find ∠STR.", "options": {"A": "30°", "B": "40°", "C": "50°", "D": "60°"}, "correct_answer": "D"},
    {"id": 85, "difficulty": "hard", "question": "Four rays OA, OB, OC, and OD are such that ∠AOB and ∠COD are vertical angles. If ∠AOB = (4x - 15)°, ∠BOC = (3x + 10)°, and ∠AOD = 150°, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "In the figure, lines AB and CD intersect at O. OE is a ray such that ∠AOE = 60°. If ∠BOD = 80°, find ∠COE.", "options": {"A": "20°", "B": "40°", "C": "60°", "D": "80°"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "If two lines intersect and form angles such that three times one angle is equal to twice its adjacent angle, find all four angles.", "options": {"A": "45°, 135°, 45°, 135°", "B": "60°, 120°, 60°, 120°", "C": "72°, 108°, 72°, 108°", "D": "80°, 100°, 80°, 100°"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "∠A, ∠B, and ∠C are three angles at a point where OA, OB, and OC are three rays. If ∠A and ∠B are vertical angles, ∠A = (2x + 30)°, ∠B = (3x - 20)°, and ∠C = 100°, find x.", "options": {"A": "30", "B": "40", "C": "50", "D": "60"}, "correct_answer": "C"},
    {"id": 89, "difficulty": "hard", "question": "Lines LM and NO intersect at P. A ray PQ bisects ∠LPN. If ∠LPN = 80°, find ∠OPQ.", "options": {"A": "40°", "B": "50°", "C": "80°", "D": "100°"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "In the figure, AB and CD intersect at O. OE bisects ∠AOC. If ∠AOD = 120°, find ∠BOE.", "options": {"A": "30°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "C"},
    {"id": 91, "difficulty": "hard", "question": "If the difference between two adjacent angles forming a linear pair is 40°, and one angle is acute, find both angles.", "options": {"A": "50° and 90°", "B": "60° and 100°", "C": "70° and 110°", "D": "80° and 120°"}, "correct_answer": "C"},
    {"id": 92, "difficulty": "hard", "question": "Three lines intersect at point O forming six angles. If two vertical angle pairs are in the ratio 2:3 and 3:4, and the smallest angle is 40°, find the largest angle.", "options": {"A": "80°", "B": "100°", "C": "120°", "D": "140°"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "In the figure, lines PQ, RS, and TU intersect at O. If ∠POT = 50°, ∠QOR = 70°, and RS is a straight line, find ∠SOT.", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "If ∠A and ∠B are vertical angles, and ∠C and ∠D are their adjacent angles respectively. If ∠A + ∠C = 210°, find ∠B.", "options": {"A": "30°", "B": "60°", "C": "120°", "D": "150°"}, "correct_answer": "D"},
    {"id": 95, "difficulty": "hard", "question": "Lines AB and CD intersect at O. Ray OE bisects ∠AOC and ray OF bisects ∠BOD. If ∠AOC = 80°, find ∠EOF.", "options": {"A": "40°", "B": "80°", "C": "90°", "D": "100°"}, "correct_answer": "C"},
    {"id": 96, "difficulty": "hard", "question": "In a figure, four lines intersect at a single point forming eight angles. If two vertically opposite angles are 55° each, and the remaining angles are in arithmetic progression, find the smallest angle.", "options": {"A": "25°", "B": "35°", "C": "45°", "D": "55°"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "If two lines intersect and form angles such that one angle is 20° more than three times its adjacent angle, find the measure of the acute angles formed.", "options": {"A": "30°", "B": "40°", "C": "50°", "D": "60°"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "∠X and ∠Y are vertical angles. ∠Z is adjacent to both. If ∠X = (5a - 10)°, ∠Y = (3a + 30)°, and ∠Z = (4a + 20)°, find the value of a.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "In the figure, lines AB, CD, and EF intersect at O. If ∠AOC : ∠COE = 3:2 and ∠BOD = 60°, find ∠COE.", "options": {"A": "36°", "B": "48°", "C": "60°", "D": "72°"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "If the sum of two adjacent angles is 180° and their difference is 40°, and they are not a linear pair (they share only vertex, not side), find the larger angle.", "options": {"A": "70°", "B": "90°", "C": "110°", "D": "130°"}, "correct_answer": "C"}
  , {"id":101,"difficulty":"easy","question":"If two angles share a common vertex and one common arm, they are called:","options":{"A":"Vertical angles","B":"Adjacent angles","C":"Supplementary angles","D":"Complementary angles"},"correct_answer":"B"},
    {"id":102,"difficulty":"easy","question":"Vertical angles are formed when:","options":{"A":"Two parallel lines intersect","B":"Two lines intersect","C":"A ray bisects an angle","D":"Two angles form a triangle"},"correct_answer":"B"},
    {"id":103,"difficulty":"easy","question":"If one vertical angle is 38°, the other vertical angle is:","options":{"A":"38°","B":"52°","C":"142°","D":"180°"},"correct_answer":"A"},
    {"id":104,"difficulty":"easy","question":"Adjacent angles always share:","options":{"A":"Only a vertex","B":"Only a side","C":"A vertex and a side","D":"Neither vertex nor side"},"correct_answer":"C"},
    {"id":105,"difficulty":"easy","question":"If two adjacent angles form a straight line, their sum is:","options":{"A":"90°","B":"120°","C":"180°","D":"360°"},"correct_answer":"C"},
    {"id":106,"difficulty":"easy","question":"Which of the following angles are always equal?","options":{"A":"Adjacent angles","B":"Linear pair angles","C":"Vertical angles","D":"Complementary angles"},"correct_answer":"C"},
    {"id":107,"difficulty":"easy","question":"If two lines intersect, how many angles are formed?","options":{"A":"2","B":"3","C":"4","D":"6"},"correct_answer":"C"},
    {"id":108,"difficulty":"easy","question":"Can two obtuse angles be vertical angles?","options":{"A":"Yes","B":"No","C":"Only sometimes","D":"Only if equal"},"correct_answer":"A"},
    {"id":109,"difficulty":"easy","question":"If ∠A and ∠B are adjacent and ∠A = 45°, ∠B = 45°, they are:","options":{"A":"Vertical angles","B":"Complementary angles","C":"Supplementary angles","D":"Reflex angles"},"correct_answer":"B"},
    {"id":110,"difficulty":"easy","question":"Two angles opposite each other when lines intersect are called:","options":{"A":"Adjacent","B":"Linear pair","C":"Vertical","D":"Complementary"},"correct_answer":"C"},

    {"id":111,"difficulty":"medium","question":"Two lines intersect. If one angle is 64°, find its adjacent angle.","options":{"A":"64°","B":"116°","C":"90°","D":"180°"},"correct_answer":"B"},
    {"id":112,"difficulty":"medium","question":"If two vertical angles are (3x + 15)° and (5x - 25)°, find x.","options":{"A":"5","B":"10","C":"15","D":"20"},"correct_answer":"B"},
    {"id":113,"difficulty":"medium","question":"Two adjacent angles form a linear pair. If one angle is 72°, find the other.","options":{"A":"72°","B":"108°","C":"90°","D":"36°"},"correct_answer":"B"},
    {"id":114,"difficulty":"medium","question":"If ∠A and ∠B are vertical angles and ∠A = 3y + 15, ∠B = 2y + 45, find y.","options":{"A":"10","B":"15","C":"20","D":"25"},"correct_answer":"B"},
    {"id":115,"difficulty":"medium","question":"Two adjacent angles are in the ratio 2:3 and form a straight line. Find the larger angle.","options":{"A":"72°","B":"90°","C":"108°","D":"120°"},"correct_answer":"C"},
    {"id":116,"difficulty":"medium","question":"If one angle of a linear pair is 25° less than the other, find the smaller angle.","options":{"A":"65°","B":"77.5°","C":"87.5°","D":"90°"},"correct_answer":"B"},
    {"id":117,"difficulty":"medium","question":"If vertical angles are (4x − 10)° and (2x + 30)°, find the measure of each angle.","options":{"A":"50°","B":"60°","C":"70°","D":"80°"},"correct_answer":"C"},
    {"id":118,"difficulty":"medium","question":"Two adjacent angles are complementary. If one is 38°, find the other.","options":{"A":"38°","B":"42°","C":"52°","D":"62°"},"correct_answer":"B"},
    {"id":119,"difficulty":"medium","question":"If one angle formed by intersecting lines is obtuse, the vertically opposite angle is:","options":{"A":"Acute","B":"Right","C":"Obtuse","D":"Straight"},"correct_answer":"C"},
    {"id":120,"difficulty":"medium","question":"The sum of two vertically opposite angles is 140°. Find each angle.","options":{"A":"70°","B":"40°","C":"90°","D":"110°"},"correct_answer":"A"},

    {"id":121,"difficulty":"medium","question":"If ∠X and ∠Y are adjacent and ∠X = 2∠Y and they form a linear pair, find ∠Y.","options":{"A":"30°","B":"45°","C":"60°","D":"90°"},"correct_answer":"A"},
    {"id":122,"difficulty":"medium","question":"Two lines intersect. If one angle is (x + 20)° and its vertical angle is (3x − 40)°, find x.","options":{"A":"20","B":"25","C":"30","D":"35"},"correct_answer":"C"},
    {"id":123,"difficulty":"medium","question":"Find the angle adjacent to 128° when two lines intersect.","options":{"A":"52°","B":"62°","C":"72°","D":"92°"},"correct_answer":"A"},
    {"id":124,"difficulty":"medium","question":"If vertical angles are equal and one is 95°, how many angles formed are obtuse?","options":{"A":"1","B":"2","C":"3","D":"4"},"correct_answer":"B"},
    {"id":125,"difficulty":"medium","question":"Two adjacent angles are supplementary. If one is thrice the other, find the smaller angle.","options":{"A":"30°","B":"45°","C":"60°","D":"90°"},"correct_answer":"A"},
    {"id":126,"difficulty":"medium","question":"If the difference between two adjacent supplementary angles is 20°, find the larger angle.","options":{"A":"80°","B":"90°","C":"100°","D":"110°"},"correct_answer":"C"},
    {"id":127,"difficulty":"medium","question":"Vertical angles are equal because they are formed by:","options":{"A":"Parallel lines","B":"Straight lines","C":"Intersecting lines","D":"Perpendicular bisectors"},"correct_answer":"C"},
    {"id":128,"difficulty":"medium","question":"If two lines intersect at right angles, all angles formed are:","options":{"A":"45°","B":"90°","C":"120°","D":"180°"},"correct_answer":"B"},
    {"id":129,"difficulty":"medium","question":"If ∠A and ∠B are vertical angles and ∠A + ∠B = 180°, find ∠A.","options":{"A":"45°","B":"60°","C":"90°","D":"120°"},"correct_answer":"C"},
    {"id":130,"difficulty":"medium","question":"Two adjacent angles are (x − 10)° and (2x + 20)°. If they form a linear pair, find x.","options":{"A":"40","B":"50","C":"60","D":"70"},"correct_answer":"B"},

    {"id":131,"difficulty":"hard","question":"Three lines intersect at a point forming six angles. If one angle is 30°, find all other angles.","options":{"A":"30°, 30°, 150°, 150°, 150°","B":"30°, 30°, 30°, 150°, 150°","C":"30°, 150°, 30°, 150°, 30°","D":"30°, 30°, 150°, 150°, 30°"},"correct_answer":"A"},
    {"id":132,"difficulty":"hard","question":"If two vertical angles are in the ratio 3:5, find the acute angle.","options":{"A":"45°","B":"54°","C":"67.5°","D":"75°"},"correct_answer":"C"},
    {"id":133,"difficulty":"hard","question":"The sum of two adjacent angles is 180° and their ratio is 4:5. Find the obtuse angle.","options":{"A":"80°","B":"100°","C":"120°","D":"140°"},"correct_answer":"B"},
    {"id":134,"difficulty":"hard","question":"Two lines intersect. One angle is 20° more than its vertically opposite angle. Find all angles.","options":{"A":"80°, 100°","B":"90°, 90°","C":"70°, 110°","D":"60°, 120°"},"correct_answer":"B"},
    {"id":135,"difficulty":"hard","question":"If two adjacent angles are supplementary and one is twice the other, find the smaller angle.","options":{"A":"45°","B":"60°","C":"90°","D":"120°"},"correct_answer":"A"},
    {"id":136,"difficulty":"hard","question":"If three angles at a point are equal and the fourth angle is 90°, find each of the equal angles.","options":{"A":"30°","B":"45°","C":"60°","D":"90°"},"correct_answer":"A"},
    {"id":137,"difficulty":"hard","question":"Two vertical angles are each (5x − 15)°. If their sum is 170°, find x.","options":{"A":"10","B":"12","C":"17","D":"20"},"correct_answer":"B"},
    {"id":138,"difficulty":"hard","question":"If the acute angle formed by two intersecting lines is 40°, find the obtuse angle.","options":{"A":"40°","B":"60°","C":"120°","D":"140°"},"correct_answer":"C"},
    {"id":139,"difficulty":"hard","question":"Two adjacent angles differ by 30° and form a straight line. Find both angles.","options":{"A":"75° and 105°","B":"60° and 120°","C":"45° and 135°","D":"90° and 90°"},"correct_answer":"A"},
    {"id":140,"difficulty":"hard","question":"If one vertical angle is (2x + 10)° and its adjacent angle is (3x − 20)°, find x.","options":{"A":"20","B":"30","C":"40","D":"50"},"correct_answer":"B"},

    {"id":141,"difficulty":"hard","question":"Four rays form four angles at a point. If two vertically opposite angles are 65° each, find the other two angles.","options":{"A":"65° each","B":"115° each","C":"125° each","D":"180° each"},"correct_answer":"B"},
    {"id":142,"difficulty":"hard","question":"If the ratio of two adjacent supplementary angles is 7:11, find the smaller angle.","options":{"A":"56°","B":"63°","C":"70°","D":"77°"},"correct_answer":"A"},
    {"id":143,"difficulty":"hard","question":"The sum of three angles formed at a point is 270°. If two are vertical angles of 80° each, find the third angle.","options":{"A":"70°","B":"90°","C":"110°","D":"130°"},"correct_answer":"A"},
    {"id":144,"difficulty":"hard","question":"If two lines intersect and one angle is (x + 20)° and the adjacent angle is (3x − 40)°, find x.","options":{"A":"40","B":"50","C":"60","D":"70"},"correct_answer":"C"},
    {"id":145,"difficulty":"hard","question":"Two vertical angles are supplementary. Find each angle.","options":{"A":"45°","B":"60°","C":"90°","D":"120°"},"correct_answer":"C"},
    {"id":146,"difficulty":"hard","question":"If three adjacent angles on a straight line are equal, find each angle.","options":{"A":"45°","B":"60°","C":"90°","D":"120°"},"correct_answer":"B"},
    {"id":147,"difficulty":"hard","question":"The difference between two vertical angles is zero. What does this imply?","options":{"A":"They are complementary","B":"They are equal","C":"They are supplementary","D":"They are adjacent"},"correct_answer":"B"},
    {"id":148,"difficulty":"hard","question":"If one angle formed by intersecting lines is reflex, what can be said about its vertical angle?","options":{"A":"It is acute","B":"It is obtuse","C":"It is reflex","D":"It is right"},"correct_answer":"C"},
    {"id":149,"difficulty":"hard","question":"If the sum of four angles formed by intersecting lines is divided equally, find each angle.","options":{"A":"45°","B":"60°","C":"90°","D":"120°"},"correct_answer":"C"},
    {"id":150,"difficulty":"hard","question":"Two adjacent angles form a straight line and differ by 50°. Find the larger angle.","options":{"A":"65°","B":"115°","C":"130°","D":"155°"},"correct_answer":"B"}

]
}