Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 894 · 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. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 125° (c) 35° (d) 305°
2. 2.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 60° (c) 150° (d) 30°
3. 3.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 155° (b) 110° (c) 135° (d) 70°
4. 4.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 290° (c) 35° (d) 145°
5. 5.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 30° (c) 20° (d) 140°
6. 6.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 155° (b) 55° (c) 30° (d) 150°
7. 7.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 80° (c) 155° (d) 100°
8. 8.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 30° (b) 50° (c) 150° (d) 160°
9. 9.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 65° (b) 150° (c) 115° (d) 145°
10. 10.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 136° (c) 45° (d) 135°
11. 11.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 70° (d) 60°
12. 12.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 125° (d) 85°
13. 13.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
14. 14.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 85° (b) 140° (c) 135° (d) 95°
15. 15.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 25° (c) 65° (d) 155°
16. 16.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 140° (b) 220° (c) 40° (d) 41°
17. 17.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 70° (b) 250° (c) 140° (d) 110°
18. 18.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 30° (d) 75°
19. 19.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 255° (b) 75° (c) 105° (d) 150°
20. 20.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 90° (b) 110° (c) 20° (d) 160°
21. 21.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 80° (c) 70° (d) 160°
22. 22.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 145° (b) 65° (c) 100° (d) 115°
23. 23.Two angles of a triangle are 55° and 50°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 130° (d) 125°
24. 24.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 75° (c) 105° (d) 160°
25. 25.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 85° (c) 95° (d) 120°
26. 26.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 155° (b) 110° (c) 135° (d) 70°
27. 27.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) 150° (d) 60°
28. 28.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 26° (c) 25° (d) 205°
29. 29.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 25° (d) 50°
30. 30.Two angles of a triangle are 20° and 110°. What is the exterior angle at the third corner? (a) 50° (b) 70° (c) 130° (d) 160°
31. 31.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 40° (b) 165° (c) 155° (d) 15°
32. 32.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 130° (c) 35° (d) 50°
33. 33.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 85° (d) 86°
34. 34.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 75° (d) 30°
35. 35.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 30° (c) 15° (d) 150°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 150° (c) 76° (d) 75°
37. 37.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 75° (d) 100°
38. 38.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 75° (b) 45° (c) 150° (d) 135°
39. 39.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°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 40° (c) 41° (d) 80°

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