Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 863 · 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 90°. What is each of the other two angles? (a) 90° (b) 45° (c) 135° (d) 270°
2. 2.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 100° (d) 50°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 145° (c) 110° (d) 35°
4. 4.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 160° (b) 135° (c) 155° (d) 45°
5. 5.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 100° (b) 80° (c) 115° (d) 145°
6. 6.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 55° (b) 155° (c) 125° (d) 150°
7. 7.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 105° (c) 70° (d) 145°
8. 8.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 35° (b) 215° (c) 70° (d) 145°
9. 9.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 90° (b) 30° (c) 120° (d) 150°
10. 10.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 86° (c) 85° (d) 95°
11. 11.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 120° (b) 160° (c) 80° (d) 100°
12. 12.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 61° (d) 30°
13. 13.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 110° (c) 40° (d) 70°
14. 14.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 26° (c) 205° (d) 25°
15. 15.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 120° (d) 110°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 90° (c) 135° (d) 46°
17. 17.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°
18. 18.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 130° (b) 140° (c) 90° (d) 270°
19. 19.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 125° (c) 305° (d) 35°
20. 20.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 60° (d) 120°
21. 21.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 245° (d) 130°
22. 22.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 40° (b) 105° (c) 140° (d) 115°
23. 23.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 100° (b) 20° (c) 80° (d) 200°
24. 24.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 160° (c) 10° (d) 20°
25. 25.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 105° (b) 95° (c) 160° (d) 85°
26. 26.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 30° (b) 120° (c) 90° (d) 150°
27. 27.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) 65° (c) 295° (d) 115°
28. 28.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 70° (c) 35° (d) 55°
29. 29.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 110° (b) 290° (c) 70° (d) 20°
30. 30.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 75° (b) 10° (c) 115° (d) 170°
31. 31.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 250° (b) 70° (c) 140° (d) 110°
32. 32.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 130° (b) 160° (c) 70° (d) 110°
33. 33.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 20° (b) 65° (c) 160° (d) 135°
34. 34.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) 20° (c) 21° (d) 200°
35. 35.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 20° (b) 150° (c) 50° (d) 160°
36. 36.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 75° (d) 15°
37. 37.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 155° (d) 140°
38. 38.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 105° (b) 125° (c) 160° (d) 75°
39. 39.Two angles of a triangle are 40° and 95°. What is the exterior angle at the third corner? (a) 45° (b) 85° (c) 140° (d) 135°
40. 40.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 160° (b) 50° (c) 150° (d) 130°

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