Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 273 · 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 70° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 105° (c) 145° (d) 75°
2. 2.Two angles of a triangle are 40° and 105°. What is the third angle? (a) 75° (b) 145° (c) 35° (d) 140°
3. 3.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 85° (b) 15° (c) 110° (d) 165°
4. 4.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 85° (b) 160° (c) 115° (d) 95°
5. 5.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 135° (c) 45° (d) 105°
6. 6.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 40° (b) 140° (c) 150° (d) 70°
7. 7.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 46° (c) 45° (d) 55°
8. 8.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 120° (b) 55° (c) 115° (d) 125°
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) 50° (c) 40° (d) 65°
10. 10.Two angles of a triangle are 45° and 100°. What is the third angle? (a) 145° (b) 135° (c) 35° (d) 80°
11. 11.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 150° (b) 85° (c) 55° (d) 125°
12. 12.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 95° (b) 155° (c) 120° (d) 85°
13. 13.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 55° (c) 35° (d) 125°
14. 14.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 10° (d) 85°
15. 15.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 40° (c) 140° (d) 41°
16. 16.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 110° (c) 120° (d) 70°
17. 17.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 170° (c) 86° (d) 95°
18. 18.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 255° (b) 75° (c) 150° (d) 105°
19. 19.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 110° (b) 155° (c) 95° (d) 85°
20. 20.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 100° (d) 50°
21. 21.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°
22. 22.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°
23. 23.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 70° (b) 250° (c) 140° (d) 110°
24. 24.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 105° (d) 100°
25. 25.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 70° (d) 50°
26. 26.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 105° (b) 40° (c) 115° (d) 140°
27. 27.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 155° (b) 55° (c) 80° (d) 125°
28. 28.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 145° (d) 110°
29. 29.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 35° (b) 135° (c) 145° (d) 80°
30. 30.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°
31. 31.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 85° (b) 160° (c) 105° (d) 95°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 70° (c) 140° (d) 110°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 270° (c) 135° (d) 45°
34. 34.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°
35. 35.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 110° (b) 90° (c) 160° (d) 70°
36. 36.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 150° (b) 75° (c) 255° (d) 105°
37. 37.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 80° (b) 150° (c) 100° (d) 130°
38. 38.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 80° (c) 100° (d) 10°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 290° (c) 35° (d) 145°
40. 40.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 120° (c) 40° (d) 60°

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