Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 78 · 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 70° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 110° (c) 115° (d) 65°
2. 2.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 240° (c) 60° (d) 120°
3. 3.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 130° (b) 230° (c) 50° (d) 115°
4. 4.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 45° (b) 110° (c) 115° (d) 135°
5. 5.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 30° (c) 60° (d) 150°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 55° (c) 125° (d) 110°
7. 7.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 80° (c) 50° (d) 10°
8. 8.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 160° (d) 135°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 25° (c) 310° (d) 130°
10. 10.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 135° (d) 140°
11. 11.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 75° (b) 130° (c) 25° (d) 155°
12. 12.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 155° (b) 135° (c) 25° (d) 70°
13. 13.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 25° (b) 100° (c) 155° (d) 105°
14. 14.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 85° (b) 130° (c) 50° (d) 145°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 120° (b) 121° (c) 240° (d) 60°
16. 16.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 40° (b) 140° (c) 155° (d) 65°
17. 17.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 85° (d) 125°
18. 18.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) 120° (c) 30° (d) 60°
19. 19.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 90° (b) 110° (c) 270° (d) 160°
20. 20.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 110° (b) 60° (c) 130° (d) 120°
21. 21.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 335° (c) 25° (d) 155°
22. 22.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) 81° (c) 100° (d) 260°
23. 23.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 110° (b) 95° (c) 85° (d) 155°
24. 24.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 120° (d) 100°
25. 25.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 115° (c) 270° (d) 90°
26. 26.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 75° (b) 125° (c) 130° (d) 105°
27. 27.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 60° (b) 145° (c) 120° (d) 155°
28. 28.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 155° (b) 100° (c) 75° (d) 105°
29. 29.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 150° (d) 160°
30. 30.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 50° (c) 230° (d) 130°
31. 31.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 145° (b) 60° (c) 155° (d) 120°
32. 32.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 105° (b) 85° (c) 160° (d) 95°
33. 33.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) 26° (c) 155° (d) 25°
34. 34.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 100° (c) 80° (d) 81°
35. 35.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 80° (b) 160° (c) 60° (d) 120°
36. 36.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 110° (d) 130°
37. 37.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 100° (d) 140°
38. 38.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°
39. 39.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 100° (c) 150° (d) 30°
40. 40.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 46° (b) 135° (c) 225° (d) 45°

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