Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 598 · 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 65° and 35°. What is the third angle? (a) 145° (b) 115° (c) 80° (d) 100°
2. 2.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 150° (b) 50° (c) 130° (d) 80°
3. 3.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 65° (c) 135° (d) 115°
4. 4.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 45° (b) 225° (c) 135° (d) 46°
5. 5.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 55° (d) 160°
6. 6.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 70° (b) 110° (c) 115° (d) 135°
7. 7.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 210° (c) 105° (d) 30°
8. 8.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 255° (b) 150° (c) 75° (d) 105°
9. 9.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 110° (b) 105° (c) 145° (d) 35°
10. 10.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 60° (b) 115° (c) 120° (d) 125°
11. 11.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 70° (d) 340°
12. 12.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 75° (d) 125°
13. 13.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 145° (d) 110°
14. 14.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 140° (c) 40° (d) 220°
15. 15.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 65° (b) 140° (c) 105° (d) 115°
16. 16.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 35° (b) 125° (c) 145° (d) 90°
17. 17.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 61°
18. 18.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 60° (d) 70°
19. 19.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 40° (c) 120° (d) 30°
20. 20.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 80° (d) 140°
21. 21.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 75° (c) 255° (d) 76°
22. 22.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 10° (d) 11°
23. 23.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 105° (c) 110° (d) 145°
24. 24.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 95° (c) 170° (d) 85°
25. 25.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 50° (b) 150° (c) 20° (d) 160°
26. 26.Two angles of a triangle are 25° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 155° (c) 70° (d) 110°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 40° (b) 80° (c) 41° (d) 140°
28. 28.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 140° (c) 320° (d) 160°
29. 29.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 35° (d) 70°
30. 30.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 140° (b) 50° (c) 90° (d) 130°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 290° (c) 145° (d) 110°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 150° (b) 120° (c) 300° (d) 30°
33. 33.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 60° (b) 135° (c) 105° (d) 120°
34. 34.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 30° (d) 150°
35. 35.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 250° (c) 110° (d) 70°
36. 36.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 95° (c) 85° (d) 86°
37. 37.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 230° (c) 50° (d) 130°
38. 38.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 105° (c) 75° (d) 30°
39. 39.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 110° (b) 145° (c) 105° (d) 70°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 70° (b) 71° (c) 140° (d) 110°

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