Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 427 · 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 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 90° (c) 35° (d) 145°
2. 2.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 85° (d) 145°
3. 3.Two angles of a triangle are 50° and 90°. What is the exterior angle at the third corner? (a) 130° (b) 90° (c) 140° (d) 40°
4. 4.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 50° (d) 100°
5. 5.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 120° (d) 50°
6. 6.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 265° (d) 86°
7. 7.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 260° (c) 80° (d) 130°
8. 8.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 140° (c) 160° (d) 60°
9. 9.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 115° (c) 295° (d) 65°
10. 10.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°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 140° (d) 280°
12. 12.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 150° (b) 115° (c) 145° (d) 65°
13. 13.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 15° (b) 25° (c) 30° (d) 150°
14. 14.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 160° (c) 70° (d) 110°
15. 15.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 150° (b) 120° (c) 90° (d) 270°
16. 16.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 140° (b) 65° (c) 115° (d) 155°
17. 17.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 160° (c) 65° (d) 115°
18. 18.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 160° (b) 145° (c) 20° (d) 55°
19. 19.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 145° (c) 35° (d) 55°
20. 20.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 100° (b) 55° (c) 125° (d) 135°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 250° (c) 125° (d) 70°
22. 22.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 95° (d) 85°
23. 23.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 145° (b) 75° (c) 140° (d) 105°
24. 24.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 140° (b) 120° (c) 60° (d) 100°
25. 25.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 30° (c) 210° (d) 75°
26. 26.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 155° (b) 120° (c) 85° (d) 60°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 160° (c) 80° (d) 81°
28. 28.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 215° (c) 145° (d) 35°
29. 29.Two angles of a triangle are 50° and 70°. What is the third angle? (a) 110° (b) 120° (c) 130° (d) 60°
30. 30.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 145° (b) 150° (c) 65° (d) 30°
31. 31.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 15° (c) 75° (d) 105°
32. 32.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 55° (c) 35° (d) 125°
33. 33.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 70° (c) 71° (d) 110°
34. 34.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 75° (c) 105° (d) 160°
35. 35.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 36° (d) 215°
36. 36.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 135° (b) 105° (c) 75° (d) 150°
37. 37.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 155° (b) 150° (c) 55° (d) 30°
38. 38.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 105° (d) 30°
39. 39.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 75° (b) 140° (c) 105° (d) 115°
40. 40.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 110° (c) 40° (d) 20°

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