Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 134 · 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 70°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 235° (d) 110°
2. 2.Two angles of a triangle are 25° and 100°. What is the exterior angle at the third corner? (a) 125° (b) 80° (c) 155° (d) 55°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 75° (b) 105° (c) 76° (d) 150°
4. 4.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 130° (c) 310° (d) 50°
5. 5.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 160° (d) 145°
6. 6.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 145° (d) 35°
7. 7.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 150° (b) 300° (c) 120° (d) 30°
8. 8.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 135° (b) 105° (c) 120° (d) 45°
9. 9.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 60° (d) 155°
10. 10.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 11° (d) 10°
11. 11.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 85° (b) 120° (c) 60° (d) 155°
12. 12.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°
13. 13.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 50° (d) 100°
14. 14.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 290° (b) 110° (c) 70° (d) 145°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 60° (c) 120° (d) 240°
16. 16.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 110° (b) 105° (c) 145° (d) 35°
17. 17.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 130° (b) 50° (c) 230° (d) 100°
18. 18.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 100° (d) 80°
19. 19.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 90° (c) 45° (d) 46°
20. 20.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 155° (b) 145° (c) 35° (d) 60°
21. 21.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 115° (b) 125° (c) 55° (d) 120°
22. 22.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 115° (d) 110°
23. 23.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 110° (d) 100°
24. 24.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 105° (b) 130° (c) 55° (d) 125°
25. 25.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 145° (b) 65° (c) 150° (d) 115°
26. 26.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 65° (b) 150° (c) 115° (d) 95°
27. 27.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 70° (b) 110° (c) 100° (d) 150°
28. 28.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 270° (c) 155° (d) 90°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 210° (c) 30° (d) 105°
30. 30.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 150° (c) 31° (d) 30°
31. 31.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 150° (d) 160°
32. 32.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 140° (b) 90° (c) 130° (d) 40°
33. 33.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 135° (b) 105° (c) 120° (d) 45°
34. 34.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 120° (c) 145° (d) 35°
35. 35.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 160° (c) 70° (d) 130°
36. 36.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 46° (c) 225° (d) 45°
37. 37.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 10° (c) 85° (d) 5°
38. 38.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 40° (d) 100°
39. 39.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 55° (c) 145° (d) 35°
40. 40.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 105° (d) 30°

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