Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 51 · 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 140°. What is the third angle? (a) 165° (b) 40° (c) 155° (d) 15°
2. 2.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 110° (b) 100° (c) 150° (d) 80°
3. 3.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 145° (b) 105° (c) 110° (d) 70°
4. 4.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 55° (b) 110° (c) 235° (d) 125°
5. 5.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 275° (d) 5°
6. 6.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 55° (c) 125° (d) 145°
7. 7.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 235° (b) 125° (c) 110° (d) 55°
8. 8.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 100° (d) 50°
9. 9.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) 30° (c) 31° (d) 150°
10. 10.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 105° (b) 115° (c) 140° (d) 40°
11. 11.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 150° (b) 125° (c) 95° (d) 85°
12. 12.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 125° (b) 270° (c) 145° (d) 90°
13. 13.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 140° (c) 40° (d) 20°
14. 14.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 80° (b) 145° (c) 100° (d) 115°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 150° (b) 31° (c) 60° (d) 30°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 130° (d) 260°
17. 17.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 125° (b) 160° (c) 145° (d) 55°
18. 18.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 145° (b) 75° (c) 110° (d) 105°
19. 19.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 145° (d) 105°
20. 20.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 70° (b) 50° (c) 130° (d) 160°
21. 21.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 100° (b) 150° (c) 110° (d) 80°
22. 22.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 65° (b) 130° (c) 245° (d) 115°
23. 23.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 115° (b) 95° (c) 85° (d) 150°
24. 24.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°
25. 25.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 245° (c) 66° (d) 65°
26. 26.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°
27. 27.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 110° (b) 70° (c) 140° (d) 150°
28. 28.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 265° (d) 86°
29. 29.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 145° (b) 130° (c) 85° (d) 50°
30. 30.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) 40° (d) 280°
31. 31.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 65° (b) 120° (c) 125° (d) 115°
32. 32.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 160° (c) 125° (d) 55°
33. 33.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 40°
34. 34.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 65° (b) 160° (c) 135° (d) 20°
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) 15° (c) 150° (d) 30°
36. 36.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 40° (b) 100° (c) 120° (d) 140°
37. 37.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) 20° (d) 55°
38. 38.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 80° (d) 40°
39. 39.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 110° (b) 155° (c) 135° (d) 70°
40. 40.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 125° (b) 40° (c) 140° (d) 95°

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