1. Two angles whose sum is 90° are called:
A. Supplementary angles
B. Complementary angles
C. Adjacent angles
D. Reflex angles
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Answer: B. Complementary angles
Explanation: By definition, if the sum of two angles is 90°, they are called complementary angles.
2. Two angles whose sum is 180° are called:
A. Complementary angles
B. Vertically opposite angles
C. Supplementary angles
D. Acute angles
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Answer: C. Supplementary angles
Explanation: When the sum of two angles equals 180°, they form a supplementary pair.
3. Find the complement of an angle measuring 35°.
A. 55°
B. 145°
C. 65°
D. 45°
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Answer: A. 55°
Explanation: Complementary angle = 90° - 35° = 55°.
4. Find the supplement of an angle measuring 110°.
A. 70°
B. 80°
C. 90°
D. 250°
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Answer: A. 70°
Explanation: Supplementary angle = 180° - 110° = 70°.
5. An angle which is greater than 180° but less than 360° is called a:
A. Obtuse angle
B. Straight angle
C. Reflex angle
D. Complete angle
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Answer: C. Reflex angle
Explanation: Angles lying strictly between 180° and 360° are classified as reflex angles.
6. If two intersecting lines form vertically opposite angles, then these angles are always:
A. Supplementary
B. Equal
C. Complementary
D. Unequal
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Answer: B. Equal
Explanation: According to Theorem 6.1, if two lines intersect each other, then the vertically opposite angles are equal.
7. If a ray stands on a straight line, the sum of two adjacent angles so formed is equal to:
A. 90°
B. 180°
C. 270°
D. 360°
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Answer: B. 180°
Explanation: This is Axiom 6.1 (Linear Pair Axiom): If a ray stands on a line, the sum of the two adjacent angles is 180°.
8. In a linear pair of angles, if one angle measures 65°, find the measure of the other angle.
A. 115°
B. 25°
C. 125°
D. 105°
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Answer: A. 115°
Explanation: Sum of linear pair = 180°. Other angle = 180° - 65° = 115°.
9. If two lines are parallel to a third line, then they are ________ to each other.
A. Perpendicular
B. Parallel
C. Intersecting
D. Coincident
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Answer: B. Parallel
Explanation: Lines which are parallel to the same line are parallel to each other (Theorem 6.6).
10. If a transversal intersects two parallel lines, then alternate interior angles are:
A. Supplementary
B. Complementary
C. Equal
D. Unequal
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Answer: C. Equal
Explanation: When a transversal cuts two parallel lines, each pair of alternate interior angles is equal.
11. If a transversal intersects two parallel lines, the interior angles on the same side of the transversal are:
A. Equal
B. Complementary
C. Supplementary
D. Reflex
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Answer: C. Supplementary
Explanation: Interior angles on the same side of a transversal (consecutive interior angles) sum up to 180° (supplementary).
12. The sum of all interior angles of a triangle is always equal to:
A. 90°
B. 180°
C. 270°
D. 360°
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Answer: B. 180°
Explanation: Angle Sum Property of a Triangle: The sum of the three interior angles of any triangle is 180°.
13. An exterior angle of a triangle is equal to the sum of its two:
A. Adjacent interior angles
B. Opposite interior angles
C. Exterior angles
D. Complementary angles
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Answer: B. Opposite interior angles
Explanation: Exterior Angle Theorem states that an exterior angle of a triangle equals the sum of its two interior opposite angles.
14. If the two interior opposite angles of a triangle are 45° and 65°, find its exterior angle.
A. 110°
B. 70°
C. 100°
D. 120°
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Answer: A. 110°
Explanation: Exterior angle = Sum of opposite interior angles = 45° + 65° = 110°.
15. If two complementary angles are in the ratio 2 : 3, find the angles.
A. 36° and 54°
B. 40° and 60°
C. 30° and 60°
D. 20° and 70°
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Answer: A. 36° and 54°
Explanation: Let angles be 2x and 3x. 2x + 3x = 90° ⇒ 5x = 90° ⇒ x = 18°. Angles are 2(18°) = 36° and 3(18°) = 54°.
16. If two supplementary angles are in the ratio 4 : 5, find the larger angle.
A. 80°
B. 100°
C. 90°
D. 110°
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Answer: B. 100°
Explanation: 4x + 5x = 180° ⇒ 9x = 180° ⇒ x = 20°. Larger angle = 5x = 5(20°) = 100°.
17. An angle is equal to its supplement. What is the measure of this angle?
A. 45°
B. 60°
C. 90°
D. 180°
Show Answer
Answer: C. 90°
Explanation: Let the angle be x. x + x = 180° ⇒ 2x = 180° ⇒ x = 90°.
18. An angle is equal to its complement. What is its measure?
A. 30°
B. 45°
C. 90°
D. 60°
Show Answer
Answer: B. 45°
Explanation: Let the angle be x. x + x = 90° ⇒ 2x = 90° ⇒ x = 45°.
19. If three angles at a point on a straight line are in ratio 1 : 2 : 3, what is the largest angle?
A. 30°
B. 60°
C. 90°
D. 120°
Show Answer
Answer: C. 90°
Explanation: x + 2x + 3x = 180° ⇒ 6x = 180° ⇒ x = 30°. Largest angle = 3x = 3(30°) = 90°.
20. The measure of an angle which is 30° less than its supplement is:
A. 75°
B. 105°
C. 60°
D. 45°
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Answer: A. 75°
Explanation: Let angle be x. Supplement = x + 30°. x + (x + 30°) = 180° ⇒ 2x = 150° ⇒ x = 75°.
21. In ΔABC, if ∠A = 70° and ∠B = 50°, find the measure of ∠C.
A. 50°
B. 60°
C. 70°
D. 80°
Show Answer
Answer: B. 60°
Explanation: ∠A + ∠B + ∠C = 180° ⇒ 70° + 50° + ∠C = 180° ⇒ ∠C = 180° - 120° = 60°.
22. If the angles of a triangle are in the ratio 2 : 3 : 4, find the smallest angle.
A. 20°
B. 40°
C. 60°
D. 80°
Show Answer
Answer: B. 40°
Explanation: 2x + 3x + 4x = 180° ⇒ 9x = 180° ⇒ x = 20°. Smallest angle = 2x = 2(20°) = 40°.
23. A triangle can have how many right angles?
A. At most one
B. Two
C. Three
D. None
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Answer: A. At most one
Explanation: If a triangle had two right angles (90° + 90° = 180°), the third angle would be 0°, which is impossible.
24. What is the sum of all angles formed around a single point?
A. 180°
B. 270°
C. 360°
D. 90°
Show Answer
Answer: C. 360°
Explanation: The sum of all angles completely surrounding a point equals 360° (a complete angle).
25. If two lines intersect such that one of the angles is 90°, then the other three angles are each equal to:
A. 45°
B. 90°
C. 180°
D. 60°
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Answer: B. 90°
Explanation: Vertically opposite angle is 90°, and linear pair adjacent angles are 180° - 90° = 90°. All 4 angles are 90°.
26. If two parallel lines are cut by a transversal, the bisectors of any pair of alternate interior angles are:
A. Perpendicular
B. Parallel
C. Intersecting
D. Coincident
Show Answer
Answer: B. Parallel
Explanation: The bisectors of alternate interior angles form equal alternate angles with the transversal, making them parallel.
27. If an angle is 14° more than its complement, find the angle.
A. 38°
B. 52°
C. 48°
D. 42°
Show Answer
Answer: B. 52°
Explanation: Let angle = x. x + (x - 14°) = 90° ⇒ 2x = 104° ⇒ x = 52°.
28. What is the value of reflex angle of 120°?
A. 60°
B. 240°
C. 180°
D. 300°
Show Answer
Answer: B. 240°
Explanation: Reflex angle = 360° - Given Angle = 360° - 120° = 240°.
29. In a right-angled triangle, if one acute angle is 35°, the other acute angle is:
A. 45°
B. 55°
C. 65°
D. 35°
Show Answer
Answer: B. 55°
Explanation: The two acute angles in a right-angled triangle are complementary: 90° - 35° = 55°.
30. If side BC of ΔABC is produced to D such that exterior ∠ACD = 120° and ∠B = 70°, then ∠A is:
A. 50°
B. 60°
C. 70°
D. 120°
Show Answer
Answer: A. 50°
Explanation: Exterior angle = ∠A + ∠B ⇒ 120° = ∠A + 70° ⇒ ∠A = 120° - 70° = 50°.
