Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 396 · 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 110°. What is the angle next to it on the same straight line? (a) 71° (b) 250° (c) 70° (d) 110°
2. 2.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 235° (b) 110° (c) 125° (d) 55°
3. 3.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 55° (c) 105° (d) 125°
4. 4.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 70° (d) 80°
5. 5.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 30° (c) 105° (d) 15°
6. 6.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 160° (b) 125° (c) 105° (d) 75°
7. 7.Two angles of a triangle are 25° and 120°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 60° (d) 155°
8. 8.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 61° (c) 30° (d) 60°
9. 9.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 95° (b) 130° (c) 50° (d) 135°
10. 10.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 10° (c) 11° (d) 160°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 260° (c) 80° (d) 50°
12. 12.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 105° (c) 285° (d) 15°
13. 13.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 50° (b) 26° (c) 155° (d) 25°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 140° (c) 280° (d) 40°
15. 15.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 15° (c) 30° (d) 25°
16. 16.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 30° (d) 60°
17. 17.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 45° (b) 105° (c) 135° (d) 120°
18. 18.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 135° (b) 95° (c) 140° (d) 85°
19. 19.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 140° (b) 270° (c) 130° (d) 90°
20. 20.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 160° (b) 165° (c) 35° (d) 15°
21. 21.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 30° (b) 110° (c) 150° (d) 100°
22. 22.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 125° (b) 150° (c) 155° (d) 55°
23. 23.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 95° (b) 145° (c) 130° (d) 85°
24. 24.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 80° (c) 20° (d) 100°
25. 25.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 100° (d) 125°
26. 26.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 65° (b) 245° (c) 66° (d) 115°
27. 27.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 120° (d) 85°
28. 28.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 45° (c) 90° (d) 91°
29. 29.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 65° (b) 140° (c) 105° (d) 115°
30. 30.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 45° (b) 155° (c) 135° (d) 160°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 15° (c) 165° (d) 30°
32. 32.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) 21° (c) 200° (d) 20°
33. 33.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 120° (d) 150°
34. 34.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 140° (d) 40°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 120° (c) 121° (d) 60°
36. 36.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 60° (c) 40° (d) 120°
37. 37.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 105° (b) 125° (c) 55° (d) 130°
38. 38.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 270° (b) 150° (c) 120° (d) 90°
39. 39.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 50° (d) 70°
40. 40.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 100° (c) 50° (d) 140°

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