Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 990 · 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 35° and 80°. What is the third angle? (a) 115° (b) 100° (c) 145° (d) 65°
2. 2.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 100° (c) 50° (d) 80°
3. 3.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 30° (d) 60°
4. 4.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°
5. 5.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 20° (c) 160° (d) 80°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 135° (c) 270° (d) 45°
7. 7.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 115° (c) 130° (d) 65°
8. 8.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 60° (b) 145° (c) 155° (d) 120°
9. 9.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) 55° (d) 125°
10. 10.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 300° (b) 150° (c) 60° (d) 120°
11. 11.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 60° (b) 240° (c) 120° (d) 61°
12. 12.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 80° (b) 150° (c) 130° (d) 100°
13. 13.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 50° (d) 100°
14. 14.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 190° (c) 10° (d) 170°
15. 15.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 120° (b) 60° (c) 130° (d) 110°
16. 16.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 25° (b) 90° (c) 115° (d) 155°
17. 17.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 100° (d) 145°
18. 18.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 70° (b) 160° (c) 130° (d) 50°
19. 19.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 65° (c) 115° (d) 140°
20. 20.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 40° (c) 50° (d) 130°
21. 21.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 150° (b) 100° (c) 70° (d) 110°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 30° (b) 150° (c) 31° (d) 60°
23. 23.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 50° (c) 110° (d) 130°
24. 24.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 75° (c) 15° (d) 105°
25. 25.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 55° (b) 160° (c) 35° (d) 145°
26. 26.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 145° (d) 110°
27. 27.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 26° (b) 25° (c) 155° (d) 205°
28. 28.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 90° (b) 125° (c) 270° (d) 145°
29. 29.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 160° (d) 60°
30. 30.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°
31. 31.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°
32. 32.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 115° (b) 25° (c) 65° (d) 295°
33. 33.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 95° (c) 85° (d) 115°
34. 34.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 245° (b) 65° (c) 130° (d) 115°
35. 35.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 140° (b) 75° (c) 115° (d) 105°
36. 36.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 150° (c) 210° (d) 31°
37. 37.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°
38. 38.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 70° (c) 60° (d) 120°
39. 39.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 75° (b) 140° (c) 145° (d) 105°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 75° (b) 150° (c) 105° (d) 76°

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