Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 497 · 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 60° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 140° (c) 80° (d) 120°
2. 2.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 30° (c) 31° (d) 210°
3. 3.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 15° (b) 165° (c) 115° (d) 80°
4. 4.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 40° (d) 80°
5. 5.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 25° (c) 115° (d) 65°
6. 6.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 75° (b) 120° (c) 135° (d) 105°
7. 7.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 25° (b) 155° (c) 100° (d) 105°
8. 8.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 160° (b) 145° (c) 55° (d) 20°
9. 9.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) 135° (c) 45° (d) 136°
10. 10.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 155° (b) 135° (c) 110° (d) 70°
11. 11.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 60° (c) 130° (d) 120°
12. 12.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 70° (b) 115° (c) 135° (d) 110°
13. 13.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 260° (b) 100° (c) 160° (d) 80°
14. 14.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 75° (b) 105° (c) 255° (d) 150°
15. 15.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°
16. 16.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 155° (c) 25° (d) 65°
17. 17.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 20° (c) 110° (d) 70°
18. 18.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 60° (c) 140° (d) 120°
19. 19.Two angles of a triangle are 45° and 75°. What is the exterior angle at the third corner? (a) 60° (b) 105° (c) 120° (d) 135°
20. 20.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 100° (b) 105° (c) 80° (d) 155°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 55° (c) 125° (d) 250°
22. 22.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°
23. 23.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 60° (c) 30° (d) 120°
24. 24.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 130° (b) 66° (c) 115° (d) 65°
25. 25.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 145° (d) 95°
26. 26.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 81° (d) 260°
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) 140° (c) 50° (d) 70°
28. 28.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 65° (b) 150° (c) 145° (d) 115°
29. 29.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°
30. 30.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 25° (b) 155° (c) 85° (d) 120°
31. 31.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 105° (b) 130° (c) 125° (d) 50°
32. 32.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 21° (c) 200° (d) 20°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 60° (c) 59° (d) 120°
34. 34.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 55° (b) 150° (c) 30° (d) 155°
35. 35.Two angles of a triangle are 55° and 85°. What is the exterior angle at the third corner? (a) 40° (b) 95° (c) 125° (d) 140°
36. 36.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 45° (c) 46° (d) 90°
37. 37.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°
38. 38.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 105° (c) 100° (d) 80°
39. 39.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 130° (c) 310° (d) 40°
40. 40.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) 30° (d) 300°

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