Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 724 · 40 questions

How to solve it (180 is the magic number): The three angles of a triangle add up to 180°. An exterior angle equals the sum of the two interior angles opposite it. An isosceles triangle has two equal angles, opposite its two equal sides. Angles on a straight line add up to 180°; vertically opposite angles are equal.

1. 1.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 60° (b) 145° (c) 155° (d) 120°
2. 2.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 95° (b) 140° (c) 85° (d) 135°
3. 3.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 160° (b) 270° (c) 90° (d) 110°
4. 4.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 21° (c) 200° (d) 160°
5. 5.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 150° (c) 15° (d) 25°
6. 6.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 10° (b) 190° (c) 170° (d) 11°
7. 7.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 120° (b) 65° (c) 125° (d) 115°
8. 8.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 120° (b) 150° (c) 30° (d) 90°
9. 9.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 65° (c) 140° (d) 115°
10. 10.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 120° (c) 60° (d) 59°
11. 11.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 80° (b) 100° (c) 155° (d) 125°
12. 12.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 11° (c) 20° (d) 10°
13. 13.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 150°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 150° (b) 31° (c) 30° (d) 60°
15. 15.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 100° (d) 70°
16. 16.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 250° (b) 110° (c) 70° (d) 140°
17. 17.Two angles of a triangle are 35° and 100°. What is the third angle? (a) 135° (b) 145° (c) 45° (d) 80°
18. 18.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 50° (b) 115° (c) 230° (d) 65°
19. 19.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 105° (c) 50° (d) 130°
20. 20.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 130° (c) 310° (d) 50°
21. 21.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 110° (b) 135° (c) 115° (d) 45°
22. 22.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 20° (d) 80°
23. 23.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 30° (c) 31° (d) 150°
24. 24.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 50° (b) 165° (c) 145° (d) 15°
25. 25.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 50° (d) 40°
26. 26.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 60° (d) 30°
27. 27.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 35° (c) 55° (d) 125°
28. 28.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 55° (b) 150° (c) 125° (d) 155°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 30° (c) 120° (d) 150°
30. 30.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 75° (b) 100° (c) 155° (d) 105°
31. 31.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 30° (c) 15° (d) 105°
32. 32.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 75° (c) 105° (d) 145°
33. 33.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 35° (c) 145° (d) 65°
34. 34.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 300° (d) 120°
35. 35.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 35° (b) 55° (c) 160° (d) 145°
36. 36.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 195° (c) 165° (d) 15°
37. 37.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 150° (b) 140° (c) 70° (d) 40°
38. 38.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 120° (c) 61° (d) 60°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 100° (b) 200° (c) 20° (d) 80°
40. 40.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 100° (d) 150°

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