Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 86 · 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 50°. What is the exterior angle at the third corner? (a) 80° (b) 130° (c) 260° (d) 100°
2. 2.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 5° (c) 95° (d) 85°
3. 3.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 81° (b) 260° (c) 100° (d) 80°
4. 4.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 145° (b) 70° (c) 105° (d) 110°
5. 5.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) 295° (c) 115° (d) 65°
6. 6.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 30° (d) 40°
7. 7.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 125° (d) 140°
8. 8.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 150° (b) 130° (c) 160° (d) 50°
9. 9.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) 80° (d) 100°
10. 10.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 125° (b) 115° (c) 120° (d) 60°
11. 11.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 130° (b) 125° (c) 55° (d) 105°
12. 12.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 110° (b) 40° (c) 140° (d) 220°
13. 13.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 70° (d) 140°
14. 14.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 130° (b) 60° (c) 120° (d) 110°
15. 15.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 110° (b) 160° (c) 270° (d) 90°
16. 16.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°
17. 17.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 100° (c) 70° (d) 150°
18. 18.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°
19. 19.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 35° (c) 70° (d) 45°
20. 20.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 61° (c) 120° (d) 60°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 30° (c) 210° (d) 105°
22. 22.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 125° (b) 55° (c) 110° (d) 235°
23. 23.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 60° (c) 120° (d) 61°
24. 24.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 110° (b) 140° (c) 70° (d) 250°
25. 25.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 155° (b) 70° (c) 135° (d) 110°
26. 26.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 130° (c) 95° (d) 85°
27. 27.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 125° (b) 120° (c) 115° (d) 65°
28. 28.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 160° (c) 20° (d) 70°
29. 29.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 130° (b) 55° (c) 125° (d) 105°
30. 30.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 70° (b) 110° (c) 250° (d) 140°
31. 31.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°
32. 32.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 100° (d) 40°
33. 33.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 70° (d) 80°
34. 34.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 315° (c) 136° (d) 135°
35. 35.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 25° (b) 65° (c) 155° (d) 140°
36. 36.Two angles of a triangle are 30° and 70°. What is the exterior angle at the third corner? (a) 80° (b) 110° (c) 150° (d) 100°
37. 37.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 65° (b) 160° (c) 115° (d) 85°
38. 38.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 80° (b) 150° (c) 100° (d) 130°
39. 39.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 100° (b) 110° (c) 30° (d) 150°
40. 40.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 65° (b) 40° (c) 140° (d) 155°

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