Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 321 · 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 45° and 65°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 115° (d) 70°
2. 2.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 145° (b) 70° (c) 290° (d) 110°
3. 3.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 130° (b) 51° (c) 230° (d) 50°
4. 4.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 50° (b) 125° (c) 105° (d) 130°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 170° (c) 11° (d) 20°
6. 6.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 35° (b) 36° (c) 145° (d) 215°
7. 7.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 160° (b) 140° (c) 60° (d) 120°
8. 8.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 65° (b) 245° (c) 130° (d) 115°
9. 9.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 130° (d) 85°
10. 10.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 120° (b) 140° (c) 40° (d) 100°
11. 11.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 130° (d) 65°
12. 12.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 70° (b) 250° (c) 110° (d) 140°
13. 13.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 60° (b) 110° (c) 120° (d) 130°
14. 14.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 100° (c) 50° (d) 80°
15. 15.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 35° (d) 70°
16. 16.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 50° (d) 80°
17. 17.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 140° (b) 80° (c) 100° (d) 120°
18. 18.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 30° (c) 60° (d) 120°
19. 19.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 145° (c) 110° (d) 55°
20. 20.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 110° (b) 250° (c) 140° (d) 70°
21. 21.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°
22. 22.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 20° (c) 110° (d) 70°
23. 23.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 170° (c) 95° (d) 85°
24. 24.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 135° (b) 155° (c) 45° (d) 70°
25. 25.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 65° (d) 50°
26. 26.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 40° (c) 80° (d) 130°
27. 27.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 150° (b) 85° (c) 125° (d) 55°
28. 28.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 90° (b) 20° (c) 160° (d) 110°
29. 29.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 120° (b) 150° (c) 90° (d) 270°
30. 30.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) 305° (c) 35° (d) 125°
31. 31.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) 270° (d) 135°
32. 32.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 330° (c) 60° (d) 150°
33. 33.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 90° (d) 45°
34. 34.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 60° (c) 30° (d) 150°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 81° (c) 80° (d) 100°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 36° (b) 35° (c) 70° (d) 145°
37. 37.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 215° (b) 35° (c) 145° (d) 70°
38. 38.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 95° (b) 135° (c) 85° (d) 130°
39. 39.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 60° (b) 135° (c) 120° (d) 105°
40. 40.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 65° (b) 120° (c) 125° (d) 115°

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