Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 168 · 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 55° and 40°. What is the third angle? (a) 85° (b) 140° (c) 95° (d) 125°
2. 2.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 120° (d) 125°
3. 3.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 100° (d) 140°
4. 4.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 150° (b) 75° (c) 45° (d) 135°
5. 5.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 55° (d) 35°
6. 6.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 135° (b) 105° (c) 75° (d) 150°
7. 7.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 155° (b) 115° (c) 140° (d) 65°
8. 8.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 55° (c) 45° (d) 46°
9. 9.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 50° (d) 40°
10. 10.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 40° (c) 100° (d) 80°
11. 11.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 140° (b) 65° (c) 155° (d) 25°
12. 12.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 120° (b) 75° (c) 165° (d) 15°
13. 13.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 110° (d) 35°
14. 14.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 120° (c) 300° (d) 60°
15. 15.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 320° (c) 50° (d) 40°
16. 16.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 70° (b) 110° (c) 140° (d) 150°
17. 17.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 70° (b) 140° (c) 150° (d) 40°
18. 18.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 120° (d) 30°
19. 19.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 115° (c) 65° (d) 130°
20. 20.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 125° (c) 70° (d) 55°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 15° (c) 16° (d) 165°
22. 22.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 115° (c) 50° (d) 25°
23. 23.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 120° (b) 110° (c) 50° (d) 130°
24. 24.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 40° (d) 80°
25. 25.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 275° (c) 5° (d) 95°
26. 26.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 145° (b) 60° (c) 120° (d) 155°
27. 27.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 75° (d) 140°
28. 28.Two angles of a triangle are 65° and 40°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 115° (d) 105°
29. 29.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 110° (d) 130°
30. 30.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 70° (b) 135° (c) 25° (d) 155°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 61° (c) 120° (d) 60°
32. 32.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 255° (b) 105° (c) 150° (d) 75°
33. 33.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 50° (d) 110°
34. 34.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 110° (b) 235° (c) 55° (d) 125°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 250° (c) 70° (d) 125°
36. 36.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 65° (c) 335° (d) 25°
37. 37.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 75° (c) 76° (d) 150°
38. 38.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 16° (c) 195° (d) 165°
39. 39.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 140° (d) 90°
40. 40.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 130° (c) 230° (d) 50°

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