Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 366 · 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 120°. What is the angle next to it on the same straight line? (a) 60° (b) 240° (c) 61° (d) 120°
2. 2.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 70° (c) 160° (d) 20°
3. 3.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 160° (d) 125°
4. 4.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 270° (d) 150°
5. 5.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 140° (b) 220° (c) 40° (d) 110°
6. 6.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 155° (b) 50° (c) 130° (d) 310°
7. 7.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 45° (b) 160° (c) 155° (d) 135°
8. 8.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 21° (c) 20° (d) 200°
9. 9.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 215° (c) 36° (d) 35°
10. 10.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) 170° (c) 190° (d) 10°
11. 11.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 70° (d) 50°
12. 12.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 80° (c) 50° (d) 40°
13. 13.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 30° (d) 75°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 16° (c) 165° (d) 30°
15. 15.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) 71° (c) 110° (d) 250°
16. 16.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 46° (c) 45° (d) 55°
17. 17.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 65° (b) 155° (c) 40° (d) 140°
18. 18.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 105° (c) 15° (d) 75°
19. 19.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 40° (c) 140° (d) 280°
20. 20.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 115° (b) 140° (c) 105° (d) 40°
21. 21.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 155° (d) 100°
22. 22.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) 136° (c) 45° (d) 315°
23. 23.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 120° (b) 115° (c) 55° (d) 125°
24. 24.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 155° (d) 25°
25. 25.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 105° (b) 25° (c) 155° (d) 100°
26. 26.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 10° (b) 170° (c) 60° (d) 130°
27. 27.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 45° (c) 35° (d) 70°
28. 28.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 90° (c) 45° (d) 135°
29. 29.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 160° (b) 120° (c) 80° (d) 60°
30. 30.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 115° (b) 35° (c) 100° (d) 145°
31. 31.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 100° (c) 80° (d) 20°
32. 32.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 15° (b) 160° (c) 165° (d) 35°
33. 33.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 140° (b) 40° (c) 105° (d) 115°
34. 34.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 130° (d) 110°
35. 35.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 120° (b) 60° (c) 115° (d) 125°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 210° (c) 75° (d) 30°
37. 37.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 15° (b) 165° (c) 40° (d) 155°
38. 38.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 115° (b) 65° (c) 160° (d) 135°
39. 39.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 340° (d) 70°
40. 40.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 70° (b) 110° (c) 150° (d) 100°

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