Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 669 · 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 25° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 70° (c) 110° (d) 155°
2. 2.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 45° (b) 150° (c) 75° (d) 135°
3. 3.Two angles of a triangle are 40° and 110°. What is the third angle? (a) 30° (b) 150° (c) 140° (d) 70°
4. 4.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 10° (b) 110° (c) 170° (d) 80°
5. 5.Two angles of a triangle are 40° and 80°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 120° (d) 60°
6. 6.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 155° (b) 310° (c) 50° (d) 130°
7. 7.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 145° (b) 75° (c) 140° (d) 40°
8. 8.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 150° (b) 135° (c) 30° (d) 75°
9. 9.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) 20° (c) 200° (d) 21°
10. 10.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 140° (b) 155° (c) 25° (d) 65°
11. 11.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 135° (c) 91° (d) 45°
12. 12.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 150° (c) 15° (d) 30°
13. 13.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 235° (c) 125° (d) 55°
14. 14.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 35° (c) 55° (d) 145°
15. 15.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 30° (d) 120°
16. 16.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 140° (b) 250° (c) 110° (d) 70°
17. 17.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 155° (c) 25° (d) 26°
18. 18.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 85° (d) 150°
19. 19.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 30° (b) 100° (c) 150° (d) 110°
20. 20.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 45° (c) 225° (d) 135°
21. 21.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 170° (c) 190° (d) 10°
22. 22.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 71° (c) 250° (d) 70°
23. 23.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 85° (b) 95° (c) 115° (d) 160°
24. 24.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 51° (c) 130° (d) 50°
25. 25.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 65° (d) 130°
26. 26.Two angles of a triangle are 50° and 110°. What is the third angle? (a) 160° (b) 130° (c) 70° (d) 20°
27. 27.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 135° (b) 100° (c) 125° (d) 45°
28. 28.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 11° (b) 10° (c) 170° (d) 20°
29. 29.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 150° (c) 65° (d) 145°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 10° (c) 85° (d) 95°
31. 31.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 70° (c) 55° (d) 20°
32. 32.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) 220° (d) 40°
33. 33.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 105° (b) 85° (c) 160° (d) 95°
34. 34.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 115° (d) 70°
35. 35.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 95° (b) 120° (c) 85° (d) 155°
36. 36.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 120° (b) 135° (c) 105° (d) 75°
37. 37.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 65° (d) 130°
38. 38.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 60° (c) 30° (d) 120°
39. 39.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 70° (d) 60°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 35° (c) 110° (d) 145°

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