Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 532 · 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. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 325° (c) 145° (d) 55°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 80° (c) 100° (d) 160°
3. 3.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 30° (d) 120°
4. 4.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 230° (b) 130° (c) 50° (d) 100°
5. 5.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 155° (b) 65° (c) 115° (d) 140°
6. 6.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 135° (b) 115° (c) 110° (d) 65°
7. 7.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 140° (b) 100° (c) 280° (d) 40°
8. 8.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 90° (b) 110° (c) 160° (d) 270°
9. 9.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 140° (c) 40° (d) 220°
10. 10.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 150° (c) 30° (d) 60°
11. 11.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 70° (b) 125° (c) 15° (d) 165°
12. 12.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 55° (b) 20° (c) 145° (d) 160°
13. 13.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) 130° (c) 230° (d) 50°
14. 14.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 150° (c) 31° (d) 210°
15. 15.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 65° (b) 90° (c) 155° (d) 115°
16. 16.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 150° (d) 30°
17. 17.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 50° (b) 95° (c) 130° (d) 135°
18. 18.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 145° (c) 80° (d) 135°
19. 19.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 70° (b) 110° (c) 160° (d) 90°
20. 20.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 59° (c) 60° (d) 120°
21. 21.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 155° (c) 65° (d) 140°
22. 22.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 50° (d) 100°
23. 23.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 300° (c) 30° (d) 120°
24. 24.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 10° (c) 100° (d) 20°
25. 25.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 11° (d) 10°
26. 26.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 60° (b) 115° (c) 120° (d) 125°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 71° (c) 110° (d) 70°
28. 28.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 110° (d) 145°
29. 29.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 270° (b) 155° (c) 90° (d) 115°
30. 30.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 105° (b) 115° (c) 40° (d) 140°
31. 31.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 160° (b) 130° (c) 110° (d) 70°
32. 32.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 60° (c) 120° (d) 40°
33. 33.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 105° (b) 130° (c) 125° (d) 75°
34. 34.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 220° (b) 40° (c) 140° (d) 110°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 150° (b) 31° (c) 30° (d) 60°
36. 36.Two angles of a triangle are 40° and 80°. What is the exterior angle at the third corner? (a) 60° (b) 140° (c) 120° (d) 100°
37. 37.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 260° (d) 130°
38. 38.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 85° (b) 110° (c) 15° (d) 165°
39. 39.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 130° (b) 50° (c) 145° (d) 85°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 70° (c) 55° (d) 250°

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