Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 373 · 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 40° and 70°. What is the third angle? (a) 70° (b) 140° (c) 110° (d) 250°
2. 2.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 35° (b) 115° (c) 100° (d) 145°
3. 3.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 40° (c) 60° (d) 30°
4. 4.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°
5. 5.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 65° (b) 150° (c) 115° (d) 145°
6. 6.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 215° (c) 35° (d) 70°
7. 7.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 160° (b) 65° (c) 135° (d) 45°
8. 8.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 70° (c) 20° (d) 160°
9. 9.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 65° (c) 25° (d) 130°
10. 10.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 150° (b) 95° (c) 125° (d) 85°
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) 135° (b) 136° (c) 315° (d) 45°
12. 12.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 125° (b) 55° (c) 110° (d) 235°
13. 13.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 105° (c) 75° (d) 76°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 280° (c) 140° (d) 100°
15. 15.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 85° (b) 120° (c) 25° (d) 155°
16. 16.Two angles of a triangle are 30° and 135°. What is the third angle? (a) 150° (b) 165° (c) 45° (d) 15°
17. 17.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 55° (d) 35°
18. 18.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°
19. 19.Two angles of a triangle are 55° and 75°. What is the third angle? (a) 50° (b) 130° (c) 105° (d) 125°
20. 20.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 225° (b) 135° (c) 90° (d) 45°
21. 21.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 100° (c) 155° (d) 80°
22. 22.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 70° (c) 55° (d) 110°
23. 23.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 45° (c) 46° (d) 90°
24. 24.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 40° (c) 20° (d) 140°
25. 25.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 145° (b) 135° (c) 80° (d) 100°
26. 26.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) 155° (c) 65° (d) 25°
27. 27.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 150° (d) 30°
28. 28.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 115° (b) 65° (c) 145° (d) 150°
29. 29.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 140° (d) 100°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 145° (c) 35° (d) 290°
31. 31.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 70° (d) 110°
32. 32.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 56° (c) 235° (d) 55°
33. 33.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 30° (d) 15°
34. 34.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 10° (c) 280° (d) 100°
35. 35.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 100° (b) 120° (c) 80° (d) 140°
36. 36.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 61° (d) 30°
37. 37.Two angles of a triangle are 50° and 25°. What is the third angle? (a) 130° (b) 155° (c) 105° (d) 75°
38. 38.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 125° (c) 135° (d) 100°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 160° (c) 20° (d) 320°
40. 40.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 145° (c) 150° (d) 35°

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