Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 63 · 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 30° and 100°. What is the third angle? (a) 80° (b) 50° (c) 130° (d) 150°
2. 2.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 155° (b) 60° (c) 145° (d) 35°
3. 3.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 75° (d) 110°
4. 4.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 80° (c) 10° (d) 50°
5. 5.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) 70° (d) 30°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 155° (b) 25° (c) 50° (d) 26°
7. 7.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 110° (d) 115°
8. 8.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 85° (b) 155° (c) 60° (d) 120°
9. 9.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 100° (d) 115°
10. 10.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 100° (b) 260° (c) 80° (d) 130°
11. 11.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 100° (d) 10°
12. 12.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 110° (b) 290° (c) 70° (d) 20°
13. 13.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 340° (c) 160° (d) 70°
14. 14.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 26° (b) 205° (c) 155° (d) 25°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 140° (c) 20° (d) 320°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 80° (c) 160° (d) 100°
17. 17.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 130° (b) 155° (c) 50° (d) 75°
18. 18.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 160° (b) 20° (c) 200° (d) 100°
19. 19.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 60° (b) 40° (c) 140° (d) 160°
20. 20.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 145° (b) 75° (c) 140° (d) 105°
21. 21.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 20° (c) 40° (d) 110°
22. 22.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 80° (c) 20° (d) 160°
23. 23.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 140° (b) 85° (c) 95° (d) 135°
24. 24.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 125° (b) 160° (c) 55° (d) 145°
25. 25.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 155° (b) 85° (c) 110° (d) 95°
26. 26.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 100° (d) 30°
27. 27.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 245° (b) 130° (c) 65° (d) 115°
28. 28.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 36° (c) 35° (d) 215°
29. 29.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 80° (c) 50° (d) 130°
30. 30.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 115° (d) 135°
31. 31.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 160° (d) 150°
32. 32.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 65° (c) 50° (d) 130°
33. 33.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 70° (d) 125°
34. 34.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 50° (c) 140° (d) 40°
35. 35.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 90° (c) 145° (d) 35°
36. 36.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 60° (b) 120° (c) 110° (d) 130°
37. 37.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 80° (b) 125° (c) 155° (d) 25°
38. 38.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 145° (b) 150° (c) 30° (d) 65°
39. 39.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 120° (d) 60°
40. 40.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 40° (b) 70° (c) 150° (d) 140°

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