Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 34 · 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 20°. What is the angle next to it on the same straight line? (a) 340° (b) 70° (c) 160° (d) 20°
2. 2.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 20° (c) 110° (d) 70°
3. 3.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) 200° (c) 20° (d) 21°
4. 4.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 30° (c) 20° (d) 40°
5. 5.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) 120° (c) 30° (d) 60°
6. 6.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 10° (b) 170° (c) 140° (d) 50°
7. 7.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 75° (b) 130° (c) 155° (d) 50°
8. 8.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 110° (b) 145° (c) 70° (d) 105°
9. 9.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 130° (b) 120° (c) 70° (d) 110°
10. 10.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 95° (c) 5° (d) 10°
11. 11.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 55° (c) 35° (d) 325°
12. 12.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 45° (d) 120°
13. 13.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 85° (c) 95° (d) 160°
14. 14.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 110° (b) 30° (c) 100° (d) 150°
15. 15.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 110° (d) 145°
16. 16.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°
17. 17.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 115° (d) 85°
18. 18.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 40°
19. 19.Two angles of a triangle are 50° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 130° (c) 95° (d) 85°
20. 20.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 270° (b) 110° (c) 90° (d) 160°
21. 21.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 115° (b) 160° (c) 135° (d) 65°
22. 22.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 110° (b) 145° (c) 105° (d) 75°
23. 23.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 230° (b) 50° (c) 115° (d) 130°
24. 24.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 220° (b) 140° (c) 40° (d) 80°
25. 25.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 65° (c) 110° (d) 115°
26. 26.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 45° (c) 135° (d) 160°
27. 27.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 235° (d) 110°
28. 28.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 90° (c) 46° (d) 45°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 100° (b) 80° (c) 20° (d) 200°
30. 30.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 95° (b) 85° (c) 130° (d) 145°
31. 31.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°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 61° (c) 59° (d) 60°
33. 33.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 30° (c) 150° (d) 120°
34. 34.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 115° (d) 230°
35. 35.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 105° (b) 55° (c) 125° (d) 130°
36. 36.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°
37. 37.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 115° (b) 140° (c) 105° (d) 65°
38. 38.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 150° (d) 270°
39. 39.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 60° (c) 240° (d) 120°
40. 40.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 90° (c) 270° (d) 125°

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