Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 142 · 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 75° and 65°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 40°
2. 2.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 160° (c) 11° (d) 20°
3. 3.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 75° (c) 76° (d) 105°
4. 4.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 160° (b) 110° (c) 70° (d) 130°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 130° (b) 155° (c) 25° (d) 310°
6. 6.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 100° (d) 40°
7. 7.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 130° (c) 150° (d) 80°
8. 8.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 10° (c) 95° (d) 85°
9. 9.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 25° (c) 15° (d) 30°
10. 10.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 155° (b) 60° (c) 120° (d) 145°
11. 11.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 245° (c) 65° (d) 115°
12. 12.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 160° (b) 65° (c) 115° (d) 135°
13. 13.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 65° (b) 150° (c) 145° (d) 115°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 95° (c) 10° (d) 190°
15. 15.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 55° (c) 125° (d) 305°
16. 16.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 120° (b) 125° (c) 115° (d) 60°
17. 17.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 145° (d) 90°
18. 18.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 60° (b) 140° (c) 160° (d) 20°
19. 19.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°
20. 20.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 90° (c) 46° (d) 45°
21. 21.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 80° (c) 10° (d) 100°
22. 22.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 145° (b) 50° (c) 85° (d) 130°
23. 23.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 100° (d) 50°
24. 24.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 105° (b) 95° (c) 20° (d) 160°
25. 25.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 40° (c) 65° (d) 130°
26. 26.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 85° (b) 40° (c) 140° (d) 135°
27. 27.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 86° (c) 170° (d) 85°
28. 28.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 25° (c) 155° (d) 65°
29. 29.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 135° (c) 70° (d) 110°
30. 30.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 35° (c) 55° (d) 145°
31. 31.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 50° (c) 130° (d) 310°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 30° (c) 150° (d) 120°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 75° (c) 105° (d) 76°
34. 34.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 100° (c) 260° (d) 80°
35. 35.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 160° (c) 340° (d) 20°
36. 36.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) 86° (c) 95° (d) 85°
37. 37.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 100° (b) 110° (c) 150° (d) 30°
38. 38.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 80° (c) 41° (d) 40°
39. 39.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 275° (d) 5°
40. 40.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 70° (d) 130°

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