Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 155 · 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 55° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 125° (d) 135°
2. 2.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 115° (b) 165° (c) 15° (d) 80°
3. 3.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 40° (c) 70° (d) 140°
4. 4.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 120° (d) 60°
5. 5.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 125° (c) 55° (d) 35°
6. 6.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) 230° (c) 130° (d) 50°
7. 7.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 40° (c) 80° (d) 50°
8. 8.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 140° (b) 70° (c) 150° (d) 40°
9. 9.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 30° (b) 105° (c) 150° (d) 210°
10. 10.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) 200° (c) 21° (d) 20°
11. 11.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 95° (b) 135° (c) 140° (d) 85°
12. 12.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 120° (b) 95° (c) 155° (d) 85°
13. 13.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 150° (b) 70° (c) 140° (d) 110°
14. 14.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 40° (b) 320° (c) 140° (d) 160°
15. 15.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 125° (b) 130° (c) 50° (d) 105°
16. 16.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 110° (c) 40° (d) 70°
17. 17.Two angles of a triangle are 25° and 85°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 155° (d) 95°
18. 18.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 340° (c) 70° (d) 160°
19. 19.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 60° (b) 210° (c) 150° (d) 30°
20. 20.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 215° (b) 35° (c) 70° (d) 145°
21. 21.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°
22. 22.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 110° (c) 20° (d) 70°
23. 23.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 65° (c) 155° (d) 25°
24. 24.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 60° (b) 59° (c) 61° (d) 120°
25. 25.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 105° (b) 125° (c) 130° (d) 75°
26. 26.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 70° (b) 15° (c) 125° (d) 165°
27. 27.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 75° (c) 15° (d) 105°
28. 28.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 105° (c) 100° (d) 80°
29. 29.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 135° (c) 91° (d) 90°
30. 30.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 30° (d) 70°
31. 31.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 65° (c) 40° (d) 130°
32. 32.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 155° (d) 60°
33. 33.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 110° (d) 60°
34. 34.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 85° (b) 125° (c) 95° (d) 140°
35. 35.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 160° (c) 115° (d) 95°
36. 36.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 280° (d) 140°
37. 37.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 100° (c) 140° (d) 120°
38. 38.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 46° (c) 55° (d) 45°
39. 39.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 135° (b) 120° (c) 105° (d) 60°
40. 40.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 80° (c) 100° (d) 10°

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