Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 161 · 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 310°. What is each of the other two angles? (a) 155° (b) 50° (c) 25° (d) 26°
2. 2.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 55° (b) 105° (c) 125° (d) 130°
3. 3.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 85° (b) 140° (c) 125° (d) 95°
4. 4.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 140° (c) 320° (d) 40°
5. 5.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 100° (d) 50°
6. 6.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 160° (d) 130°
7. 7.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 115° (b) 135° (c) 45° (d) 110°
8. 8.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 255° (b) 105° (c) 150° (d) 75°
9. 9.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 70° (c) 71° (d) 110°
10. 10.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 95° (c) 85° (d) 170°
11. 11.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 30° (d) 120°
12. 12.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 170° (b) 135° (c) 10° (d) 55°
13. 13.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 125° (b) 80° (c) 100° (d) 155°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 46° (b) 45° (c) 90° (d) 135°
15. 15.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 31° (b) 30° (c) 210° (d) 150°
16. 16.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 140° (c) 30° (d) 40°
17. 17.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 30° (b) 31° (c) 60° (d) 150°
18. 18.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 20° (b) 160° (c) 95° (d) 105°
19. 19.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 80° (c) 280° (d) 100°
20. 20.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 20° (b) 160° (c) 55° (d) 145°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 145° (b) 35° (c) 70° (d) 36°
22. 22.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 300° (c) 60° (d) 120°
23. 23.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 100° (c) 75° (d) 155°
24. 24.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 155° (c) 50° (d) 130°
25. 25.Two angles of a triangle are 45° and 120°. What is the third angle? (a) 60° (b) 135° (c) 165° (d) 15°
26. 26.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 50° (c) 130° (d) 40°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 130° (c) 155° (d) 310°
28. 28.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 85° (b) 155° (c) 60° (d) 120°
29. 29.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 210° (b) 105° (c) 150° (d) 30°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 115° (b) 65° (c) 130° (d) 66°
31. 31.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 160° (c) 70° (d) 20°
32. 32.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 70° (b) 110° (c) 135° (d) 155°
33. 33.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 85° (b) 140° (c) 95° (d) 135°
34. 34.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 130° (b) 110° (c) 120° (d) 50°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 70° (c) 220° (d) 110°
36. 36.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 90° (d) 45°
37. 37.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 35° (c) 130° (d) 50°
38. 38.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 275° (d) 5°
39. 39.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 65° (c) 66° (d) 245°
40. 40.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 145° (c) 130° (d) 50°

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