Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 118 · 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 50° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 75° (d) 130°
2. 2.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 260° (d) 160°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 210° (c) 75° (d) 105°
4. 4.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 40° (b) 75° (c) 140° (d) 145°
5. 5.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) 265° (c) 86° (d) 95°
6. 6.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 40° (c) 100° (d) 80°
7. 7.Two angles of a triangle are 35° and 100°. What is the third angle? (a) 45° (b) 145° (c) 80° (d) 135°
8. 8.Two angles of a triangle are 55° and 55°. What is the exterior angle at the third corner? (a) 110° (b) 250° (c) 70° (d) 125°
9. 9.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 20° (b) 115° (c) 85° (d) 160°
10. 10.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 105° (b) 90° (c) 165° (d) 15°
11. 11.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 110° (c) 20° (d) 70°
12. 12.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 140° (d) 50°
13. 13.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 210° (b) 60° (c) 30° (d) 150°
14. 14.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 115° (b) 120° (c) 125° (d) 60°
15. 15.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 55° (c) 70° (d) 110°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 40° (c) 80° (d) 41°
17. 17.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 100° (b) 155° (c) 80° (d) 105°
18. 18.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 10° (c) 20° (d) 11°
19. 19.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 170° (c) 86° (d) 85°
20. 20.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 155° (b) 120° (c) 85° (d) 25°
21. 21.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 250° (d) 140°
22. 22.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) 65° (d) 25°
23. 23.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 135° (b) 85° (c) 95° (d) 140°
24. 24.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 105° (b) 145° (c) 75° (d) 140°
25. 25.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 100° (b) 20° (c) 200° (d) 160°
26. 26.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 145° (c) 30° (d) 65°
27. 27.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 165° (b) 35° (c) 15° (d) 160°
28. 28.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 90° (b) 125° (c) 270° (d) 145°
29. 29.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 50° (d) 110°
30. 30.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 10° (b) 190° (c) 170° (d) 11°
31. 31.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 55° (b) 235° (c) 125° (d) 56°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 20° (b) 200° (c) 80° (d) 100°
33. 33.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 145° (b) 85° (c) 130° (d) 50°
34. 34.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 160° (b) 150° (c) 50° (d) 130°
35. 35.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 120° (b) 145° (c) 155° (d) 60°
36. 36.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 50° (b) 130° (c) 155° (d) 75°
37. 37.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 30° (c) 70° (d) 120°
38. 38.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 125° (b) 95° (c) 150° (d) 85°
39. 39.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 105° (c) 75° (d) 140°
40. 40.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 140° (b) 100° (c) 120° (d) 60°

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