Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 43 · 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 50° and 120°. What is the third angle? (a) 130° (b) 60° (c) 170° (d) 10°
2. 2.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 100° (c) 80° (d) 10°
3. 3.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 135° (b) 315° (c) 136° (d) 45°
4. 4.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 130° (d) 40°
5. 5.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 130° (c) 110° (d) 70°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 120° (c) 60° (d) 121°
7. 7.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 260° (b) 160° (c) 80° (d) 100°
8. 8.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 100° (b) 130° (c) 230° (d) 50°
9. 9.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 90° (b) 270° (c) 110° (d) 160°
10. 10.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 145° (d) 75°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 86° (c) 95° (d) 170°
12. 12.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 30° (d) 120°
13. 13.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 40° (c) 320° (d) 140°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 145° (b) 110° (c) 290° (d) 35°
15. 15.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 255° (b) 105° (c) 75° (d) 150°
16. 16.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 70° (d) 40°
17. 17.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) 140° (c) 320° (d) 40°
18. 18.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 165° (c) 15° (d) 16°
19. 19.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 110° (c) 71° (d) 250°
20. 20.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 115° (b) 50° (c) 65° (d) 230°
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) 265° (b) 95° (c) 85° (d) 86°
22. 22.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 310° (b) 130° (c) 155° (d) 50°
23. 23.Two angles of a triangle are 55° and 55°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 125° (d) 250°
24. 24.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 125° (b) 235° (c) 110° (d) 55°
25. 25.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 40° (b) 100° (c) 140° (d) 120°
26. 26.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 80° (b) 160° (c) 120° (d) 100°
27. 27.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 25° (c) 35° (d) 50°
28. 28.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 65° (b) 115° (c) 160° (d) 135°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 45° (c) 90° (d) 135°
30. 30.Two angles of a triangle are 50° and 90°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 130° (d) 90°
31. 31.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 10° (c) 280° (d) 100°
32. 32.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 60° (c) 120° (d) 70°
33. 33.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 75° (b) 155° (c) 105° (d) 130°
34. 34.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 125° (b) 140° (c) 40° (d) 95°
35. 35.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 145° (b) 150° (c) 65° (d) 30°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 41° (c) 80° (d) 40°
37. 37.Two angles of a triangle are 50° and 45°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 85° (d) 135°
38. 38.Two angles of a triangle are 40° and 50°. What is the exterior angle at the third corner? (a) 270° (b) 130° (c) 140° (d) 90°
39. 39.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 65° (c) 66° (d) 115°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 130° (b) 25° (c) 155° (d) 310°

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