Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 565 · 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 45° and 110°. What is the third angle? (a) 70° (b) 155° (c) 135° (d) 25°
2. 2.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 150° (b) 145° (c) 65° (d) 115°
3. 3.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 150° (b) 50° (c) 130° (d) 80°
4. 4.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 145° (c) 36° (d) 35°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 85° (c) 86° (d) 95°
6. 6.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 145° (d) 65°
7. 7.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°
8. 8.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 140° (c) 135° (d) 40°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 66° (c) 130° (d) 115°
10. 10.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 75° (d) 150°
11. 11.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 160° (d) 80°
12. 12.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 290° (c) 145° (d) 110°
13. 13.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 115° (c) 30° (d) 150°
14. 14.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 90° (d) 35°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 80° (c) 260° (d) 50°
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 angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 115° (c) 65° (d) 155°
18. 18.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 105° (b) 255° (c) 150° (d) 75°
19. 19.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°
20. 20.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 110° (b) 145° (c) 105° (d) 70°
21. 21.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 130° (b) 230° (c) 50° (d) 51°
22. 22.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 100° (b) 35° (c) 115° (d) 145°
23. 23.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 45° (d) 35°
24. 24.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 110° (c) 70° (d) 20°
25. 25.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 40° (d) 115°
26. 26.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 40° (d) 100°
27. 27.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) 100° (d) 80°
28. 28.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 310° (c) 50° (d) 40°
29. 29.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 90° (c) 270° (d) 160°
30. 30.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 110° (b) 145° (c) 105° (d) 70°
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 angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 50° (d) 120°
33. 33.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 150° (b) 160° (c) 20° (d) 50°
34. 34.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 155° (b) 120° (c) 60° (d) 145°
35. 35.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 90° (b) 110° (c) 160° (d) 270°
36. 36.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 120° (b) 110° (c) 130° (d) 50°
37. 37.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 140° (d) 135°
38. 38.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 130° (c) 90° (d) 270°
39. 39.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 90° (d) 55°
40. 40.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) 25° (d) 130°

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