Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 861 · 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 straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 200° (c) 160° (d) 20°
2. 2.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 160° (b) 105° (c) 95° (d) 85°
3. 3.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 65° (d) 335°
4. 4.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 140° (b) 155° (c) 40° (d) 65°
5. 5.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 50° (c) 25° (d) 35°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 150° (c) 75° (d) 76°
7. 7.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 30° (d) 75°
8. 8.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 30° (c) 330° (d) 60°
9. 9.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 110° (b) 115° (c) 135° (d) 70°
10. 10.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) 40° (d) 80°
11. 11.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 135° (c) 45° (d) 315°
12. 12.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 145° (d) 160°
13. 13.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 140° (b) 135° (c) 95° (d) 85°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 300° (c) 120° (d) 150°
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) 55° (b) 305° (c) 125° (d) 35°
16. 16.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 280° (c) 140° (d) 80°
17. 17.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 55° (c) 35° (d) 125°
18. 18.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 145° (b) 160° (c) 55° (d) 125°
19. 19.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 120° (b) 75° (c) 165° (d) 15°
20. 20.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 270° (b) 90° (c) 110° (d) 160°
21. 21.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°
22. 22.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 50° (b) 80° (c) 130° (d) 150°
23. 23.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 155° (b) 75° (c) 25° (d) 130°
24. 24.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 115° (b) 95° (c) 150° (d) 85°
25. 25.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 76° (b) 75° (c) 105° (d) 255°
26. 26.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°
27. 27.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) 140° (c) 40° (d) 41°
28. 28.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 140° (b) 90° (c) 40° (d) 130°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 20° (c) 11° (d) 170°
30. 30.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 225° (b) 135° (c) 45° (d) 46°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 40° (b) 160° (c) 21° (d) 20°
32. 32.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 140° (b) 110° (c) 250° (d) 70°
33. 33.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 110° (d) 105°
34. 34.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 145° (c) 35° (d) 110°
35. 35.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 30° (c) 140° (d) 20°
36. 36.Two angles of a triangle are 60° and 60°. What is the exterior angle at the third corner? (a) 240° (b) 121° (c) 120° (d) 60°
37. 37.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 100° (b) 60° (c) 140° (d) 120°
38. 38.Two angles of a triangle are 40° and 110°. What is the exterior angle at the third corner? (a) 30° (b) 140° (c) 70° (d) 150°
39. 39.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 40° (d) 70°
40. 40.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 30° (c) 60° (d) 61°

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