Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 2 · 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 45° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 135° (c) 70° (d) 110°
2. 2.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 150° (b) 55° (c) 85° (d) 125°
3. 3.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 40° (c) 140° (d) 50°
4. 4.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 35° (c) 145° (d) 65°
5. 5.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 75° (b) 105° (c) 140° (d) 145°
6. 6.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 95° (c) 85° (d) 155°
7. 7.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 81° (d) 260°
8. 8.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 50° (c) 310° (d) 40°
9. 9.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 30° (c) 60° (d) 120°
10. 10.Two angles of a triangle are 30° and 135°. What is the third angle? (a) 150° (b) 165° (c) 15° (d) 45°
11. 11.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 35° (c) 130° (d) 25°
12. 12.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) 30° (c) 120° (d) 60°
13. 13.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 40° (b) 65° (c) 155° (d) 140°
14. 14.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 25° (d) 130°
15. 15.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 21° (c) 160° (d) 20°
16. 16.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 135° (d) 45°
17. 17.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 90° (d) 45°
18. 18.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 120° (c) 30° (d) 70°
19. 19.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 125° (b) 270° (c) 145° (d) 90°
20. 20.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 120° (c) 30° (d) 61°
21. 21.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 105° (c) 75° (d) 100°
22. 22.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 130° (c) 110° (d) 70°
23. 23.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) 25° (c) 26° (d) 205°
24. 24.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 210° (c) 31° (d) 30°
25. 25.Two angles of a triangle are 50° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 150° (c) 130° (d) 30°
26. 26.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 85° (b) 110° (c) 95° (d) 155°
27. 27.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 105° (c) 110° (d) 145°
28. 28.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 75° (b) 120° (c) 165° (d) 15°
29. 29.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 150° (d) 110°
30. 30.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 65° (b) 100° (c) 115° (d) 145°
31. 31.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 50° (c) 100° (d) 80°
32. 32.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 5° (b) 85° (c) 95° (d) 275°
33. 33.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 100° (b) 115° (c) 80° (d) 145°
34. 34.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 80° (b) 135° (c) 145° (d) 100°
35. 35.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 40° (d) 140°
36. 36.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 100° (b) 10° (c) 280° (d) 80°
37. 37.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 15° (c) 195° (d) 165°
38. 38.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 125° (b) 120° (c) 115° (d) 65°
39. 39.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 270° (b) 110° (c) 160° (d) 90°
40. 40.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) 110° (c) 250° (d) 70°

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