Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 946 · 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 40° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 140° (c) 55° (d) 125°
2. 2.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 105° (b) 140° (c) 65° (d) 115°
3. 3.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 155° (b) 45° (c) 135° (d) 70°
4. 4.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 45° (c) 136° (d) 135°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 20° (b) 100° (c) 200° (d) 80°
6. 6.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) 80° (d) 100°
7. 7.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 40° (c) 70° (d) 20°
8. 8.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 40° (b) 120° (c) 140° (d) 100°
9. 9.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 80° (b) 100° (c) 130° (d) 150°
10. 10.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 95° (b) 125° (c) 85° (d) 150°
11. 11.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 130° (d) 145°
12. 12.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 70° (b) 215° (c) 145° (d) 35°
13. 13.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 155° (b) 50° (c) 75° (d) 130°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 20° (b) 40° (c) 160° (d) 21°
15. 15.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 75° (b) 145° (c) 110° (d) 105°
16. 16.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 40° (c) 140° (d) 50°
17. 17.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 115° (c) 25° (d) 65°
18. 18.Two angles of a triangle are 20° and 120°. What is the exterior angle at the third corner? (a) 160° (b) 40° (c) 60° (d) 140°
19. 19.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 35° (c) 70° (d) 45°
20. 20.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) 20° (c) 21° (d) 200°
21. 21.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 70° (b) 110° (c) 90° (d) 160°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 155° (c) 130° (d) 25°
23. 23.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 105° (b) 10° (c) 170° (d) 85°
24. 24.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 55° (c) 46° (d) 90°
25. 25.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 70° (b) 135° (c) 155° (d) 45°
26. 26.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 150° (d) 30°
27. 27.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 75° (b) 135° (c) 45° (d) 150°
28. 28.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 75° (b) 105° (c) 130° (d) 155°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 250° (c) 125° (d) 55°
30. 30.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 35° (c) 50° (d) 130°
31. 31.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 160° (d) 10°
32. 32.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 320° (c) 140° (d) 40°
33. 33.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) 165° (c) 15° (d) 195°
34. 34.Two angles of a triangle are 55° and 85°. What is the exterior angle at the third corner? (a) 125° (b) 95° (c) 40° (d) 140°
35. 35.Two angles of a triangle are 50° and 110°. What is the third angle? (a) 70° (b) 20° (c) 130° (d) 160°
36. 36.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 61° (c) 120° (d) 60°
37. 37.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 35° (c) 55° (d) 145°
38. 38.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 121° (c) 240° (d) 120°
39. 39.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) 125° (d) 35°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 35° (c) 290° (d) 145°

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