Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 14 · 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 straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 155° (b) 25° (c) 26° (d) 50°
2. 2.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 120° (b) 125° (c) 115° (d) 65°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 16° (c) 15° (d) 30°
4. 4.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 270° (b) 110° (c) 160° (d) 90°
5. 5.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 55° (b) 150° (c) 85° (d) 125°
6. 6.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 70° (b) 100° (c) 150° (d) 110°
7. 7.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 45° (c) 135° (d) 136°
8. 8.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 55° (c) 145° (d) 35°
9. 9.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 40°
10. 10.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 85° (c) 95° (d) 265°
11. 11.Two angles of a triangle are 40° and 110°. What is the exterior angle at the third corner? (a) 150° (b) 70° (c) 30° (d) 140°
12. 12.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 150° (b) 115° (c) 65° (d) 145°
13. 13.Two angles of a triangle are 25° and 130°. What is the third angle? (a) 205° (b) 155° (c) 25° (d) 50°
14. 14.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 45° (b) 155° (c) 135° (d) 70°
15. 15.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 155° (d) 25°
16. 16.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 145° (d) 105°
17. 17.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 65° (d) 145°
18. 18.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) 35° (c) 55° (d) 145°
19. 19.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 40° (d) 140°
20. 20.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 160° (b) 200° (c) 100° (d) 20°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 81° (c) 160° (d) 80°
22. 22.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 130° (b) 230° (c) 50° (d) 100°
23. 23.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 70° (b) 130° (c) 110° (d) 120°
24. 24.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 135° (b) 45° (c) 95° (d) 130°
25. 25.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 120° (b) 150° (c) 90° (d) 30°
26. 26.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) 150° (c) 30° (d) 31°
27. 27.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 5° (b) 275° (c) 95° (d) 85°
28. 28.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 270° (c) 90° (d) 91°
29. 29.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) 25° (c) 65° (d) 115°
30. 30.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 35° (d) 90°
31. 31.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 35° (d) 120°
32. 32.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 75° (b) 120° (c) 105° (d) 135°
33. 33.Two angles of a triangle are 50° and 100°. What is the exterior angle at the third corner? (a) 30° (b) 80° (c) 130° (d) 150°
34. 34.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 145° (b) 90° (c) 125° (d) 270°
35. 35.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 120° (b) 75° (c) 135° (d) 105°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 125° (c) 56° (d) 55°
37. 37.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 300° (d) 150°
38. 38.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) 150° (c) 60° (d) 330°
39. 39.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 125° (c) 75° (d) 160°
40. 40.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 160° (d) 260°

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