Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 65 · 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 50° and 25°. What is the third angle? (a) 155° (b) 75° (c) 105° (d) 130°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 70° (c) 110° (d) 71°
3. 3.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 145° (c) 30° (d) 65°
4. 4.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 140° (c) 280° (d) 40°
5. 5.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 40° (c) 50° (d) 310°
6. 6.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 30° (b) 105° (c) 210° (d) 150°
7. 7.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 155° (c) 130° (d) 310°
8. 8.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 115° (c) 25° (d) 65°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 50° (b) 130° (c) 100° (d) 51°
10. 10.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 85° (b) 160° (c) 105° (d) 95°
11. 11.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 65° (b) 245° (c) 130° (d) 115°
12. 12.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 130° (d) 120°
13. 13.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 60° (b) 150° (c) 30° (d) 31°
14. 14.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 35° (b) 130° (c) 85° (d) 145°
15. 15.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 125° (b) 305° (c) 55° (d) 35°
16. 16.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 330° (c) 60° (d) 150°
17. 17.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 85° (b) 135° (c) 140° (d) 40°
18. 18.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 150° (b) 145° (c) 65° (d) 30°
19. 19.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 120° (b) 20° (c) 160° (d) 80°
20. 20.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 120° (c) 150° (d) 30°
21. 21.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 160° (c) 140° (d) 120°
22. 22.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 160° (c) 85° (d) 95°
23. 23.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 125° (b) 155° (c) 55° (d) 150°
24. 24.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 65° (c) 115° (d) 50°
25. 25.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 150° (b) 55° (c) 155° (d) 25°
26. 26.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 80° (c) 100° (d) 10°
27. 27.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 50° (d) 140°
28. 28.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 105° (b) 60° (c) 120° (d) 135°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 170° (c) 85° (d) 95°
30. 30.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 20° (c) 110° (d) 70°
31. 31.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 115° (c) 155° (d) 65°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 240° (c) 120° (d) 121°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 135° (b) 270° (c) 45° (d) 90°
34. 34.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 90° (c) 160° (d) 270°
35. 35.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 155° (b) 60° (c) 25° (d) 145°
36. 36.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 35° (c) 145° (d) 135°
37. 37.Two angles of a triangle are 55° and 55°. What is the exterior angle at the third corner? (a) 70° (b) 250° (c) 125° (d) 110°
38. 38.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 75° (d) 150°
39. 39.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 10° (c) 100° (d) 80°
40. 40.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 80° (c) 50° (d) 40°

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