Lines & Angles
33 Class 6 IMO Mathematics Olympiad practice questions on lines & angles, part of the Geometry & Spatial Thinking topic area. Every question below includes the correct answer and a full explanation.
Practice this topic interactively →1. What is the sum of angles on a straight line?
- A.90°
- B.180°
- C.270°
- D.360°
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Answer: B. 180°
Angles on a straight line always add up to 180°.
2. What is the sum of angles around a point?
- A.180°
- B.270°
- C.360°
- D.400°
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Answer: C. 360°
Angles all the way around a single point add up to 360°.
3. What type of angle measures exactly 90°?
- A.Acute
- B.Right
- C.Obtuse
- D.Straight
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Answer: B. Right
An angle of exactly 90° is called a right angle.
4. Two complementary angles add up to how many degrees?
- A.45°
- B.90°
- C.180°
- D.360°
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Answer: B. 90°
Complementary angles always add up to 90°.
5. Two angles form a straight line. One is 65°. What is the other?
- A.90
- B.115
- C.105
- D.125
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Answer: B. 115
180° − 65° = 115°.
6. A triangle has angles 55° and 60°. Find the third angle.
- A.115
- B.75
- C.65
- D.55
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Answer: C. 65
180° − 55° − 60° = 65°.
7. Two angles form a straight line. One is 35°. What is the other?
- A.135
- B.155
- C.145
- D.90
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Answer: C. 145
180° − 35° = 145°.
8. Two angles form a straight line. One angle is 68°. The other angle is:
- A.102°
- B.112°
- C.118°
- D.122°
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Answer: B. 112°
180° − 68° = 112°.
9. A triangle has angles 45° and 65°. Its third angle is:
- A.60°
- B.65°
- C.70°
- D.80°
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Answer: C. 70°
180° − 45° − 65° = 70°.
10. Two angles form a straight line. One is 95°. What is the other?
- A.75°
- B.80°
- C.85°
- D.90°
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Answer: C. 85°
180° − 95° = 85°.
11. A triangle has angles 90° and 35°. What is the third angle?
- A.45°
- B.50°
- C.55°
- D.60°
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Answer: C. 55°
180° − 90° − 35° = 55°.
12. What type of angle is 130°?
- A.Acute
- B.Right
- C.Obtuse
- D.Reflex
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Answer: C. Obtuse
An angle between 90° and 180° is obtuse.
13. Two of the three angles around a point are 150° and 90°. What is the third?
- A.100°
- B.110°
- C.120°
- D.130°
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Answer: C. 120°
360° − 150° − 90° = 120°.
14. Two supplementary angles add up to how many degrees?
- A.90°
- B.120°
- C.180°
- D.360°
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Answer: C. 180°
Supplementary angles always add up to 180°.
15. One of two complementary angles is 35°. What is the other?
- A.45°
- B.50°
- C.55°
- D.60°
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Answer: C. 55°
90° − 35° = 55°.
16. One of two supplementary angles is 112°. What is the other?
- A.58°
- B.62°
- C.68°
- D.72°
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Answer: C. 68°
180° − 112° = 68°.
17. A triangle has angles 65° and 40°. Find the third angle.
- A.65
- B.75
- C.105
- D.85
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Answer: B. 75
180° − 65° − 40° = 75°.
18. Two angles form a straight line. One is 25°. What is the other?
- A.145
- B.165
- C.90
- D.155
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Answer: D. 155
180° − 25° = 155°.
19. Two angles lie on a straight line, as shown. One of them is 75°. What is the other angle?
- A.95°
- B.100°
- C.105°
- D.115°
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Answer: C. 105°
180° − 75° = 105°.
20. In the figure, two angles form a straight line. If one is 122°, find the other.
- A.48°
- B.53°
- C.58°
- D.68°
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Answer: C. 58°
180° − 122° = 58°.
21. One angle on a straight line is 33°, as shown. Find the unknown angle.
- A.137°
- B.143°
- C.147°
- D.157°
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Answer: C. 147°
180° − 33° = 147°.
22. A triangle has two angles as shown: 50° and 60°. Find the third angle.
- A.60°
- B.65°
- C.70°
- D.80°
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Answer: C. 70°
180° − 50° − 60° = 70°.
23. In a triangle, one angle is twice another, and the third angle is 60°. Find the largest angle.
- A.70°
- B.75°
- C.80°
- D.85°
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Answer: C. 80°
The other two angles sum to 120°. If they're x and 2x, then 3x=120, x=40, so the largest is 2x=80°.
24. A triangle is isosceles with two equal angles of 50° each. What is the third angle?
- A.70°
- B.75°
- C.80°
- D.85°
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Answer: C. 80°
180° − 50° − 50° = 80°.
25. What is the total angle on a straight line?
- A.360°
- B.180°
- C.45°
- D.90°
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Answer: B. 180°
Angles on a straight line always add up to 180°.
26. What is the measure of a right angle?
- A.180°
- B.360°
- C.90°
- D.45°
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Answer: C. 90°
A right angle measures exactly 90°.
27. A triangle has angles 35° and 30°. Find the third angle.
- A.115
- B.125
- C.105
- D.65
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Answer: A. 115
180° − 35° − 30° = 115°.
28. A triangle has angles 90° and 35°, as shown. What is the third angle?
- A.45°
- B.50°
- C.55°
- D.65°
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Answer: C. 55°
180° − 90° − 35° = 55°.
29. The triangle shown has two angles of 38° and 74°. Find the missing third angle.
- A.58°
- B.64°
- C.68°
- D.78°
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Answer: C. 68°
180° − 38° − 74° = 68°.
30. An angle is 4 times its complement. Find the angle.
- A.60°
- B.68°
- C.72°
- D.76°
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Answer: C. 72°
Let the angle be x. x = 4(90−x) gives 5x=360, so x=72°.
31. Two angles form a straight line. One is 45°. What is the other?
- A.135
- B.125
- C.145
- D.90
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Answer: A. 135
180° − 45° = 135°.
32. What is the angle around a point?
- A.180°
- B.90°
- C.45°
- D.360°
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Answer: D. 360°
Angles all the way around a point always add up to 360°.
33. Two angles form a straight line. One is 75°. What is the other?
- A.90
- B.95
- C.105
- D.115
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Answer: C. 105
180° − 75° = 105°.