Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 404 · 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 300°. What is each of the other two angles? (a) 31° (b) 60° (c) 150° (d) 30°
2. 2.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 71° (c) 70° (d) 250°
3. 3.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 150° (b) 160° (c) 130° (d) 50°
4. 4.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 140° (b) 15° (c) 55° (d) 165°
5. 5.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 120° (b) 75° (c) 135° (d) 105°
6. 6.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 110° (b) 290° (c) 145° (d) 70°
7. 7.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 130° (d) 145°
8. 8.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 120° (c) 100° (d) 160°
9. 9.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 36° (b) 35° (c) 215° (d) 145°
10. 10.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 65° (b) 145° (c) 115° (d) 150°
11. 11.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 80° (b) 125° (c) 155° (d) 100°
12. 12.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 85° (b) 155° (c) 120° (d) 95°
13. 13.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 105° (b) 155° (c) 75° (d) 100°
14. 14.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 60° (b) 140° (c) 160° (d) 120°
15. 15.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 30° (c) 60° (d) 120°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 270° (c) 90° (d) 135°
17. 17.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 100° (c) 280° (d) 80°
18. 18.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 110° (c) 20° (d) 40°
19. 19.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 155° (c) 26° (d) 25°
20. 20.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 115° (b) 40° (c) 105° (d) 140°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 10° (c) 170° (d) 11°
22. 22.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 65° (b) 295° (c) 25° (d) 115°
23. 23.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 20° (c) 160° (d) 80°
24. 24.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 95° (b) 110° (c) 25° (d) 155°
25. 25.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 230° (c) 130° (d) 50°
26. 26.Two angles of a triangle are 45° and 120°. What is the third angle? (a) 165° (b) 15° (c) 60° (d) 135°
27. 27.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 125° (d) 130°
28. 28.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 25° (c) 155° (d) 65°
29. 29.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 30° (c) 150° (d) 60°
30. 30.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°
31. 31.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 90° (c) 91° (d) 135°
32. 32.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 30° (c) 120° (d) 60°
33. 33.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 130° (b) 55° (c) 125° (d) 105°
34. 34.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 235° (c) 110° (d) 55°
35. 35.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 150° (d) 140°
36. 36.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 40° (b) 200° (c) 160° (d) 20°
37. 37.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 10° (d) 85°
38. 38.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 105° (b) 65° (c) 115° (d) 140°
39. 39.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 140° (b) 130° (c) 90° (d) 270°
40. 40.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 110° (b) 140° (c) 70° (d) 150°

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