Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 70 · 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. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 105° (c) 30° (d) 210°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 140° (c) 20° (d) 320°
3. 3.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 35° (d) 110°
4. 4.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 30° (d) 60°
5. 5.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 110° (c) 150° (d) 70°
6. 6.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 30° (d) 60°
7. 7.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 130° (b) 120° (c) 70° (d) 110°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 250° (c) 70° (d) 55°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 120° (c) 60° (d) 240°
10. 10.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 85° (b) 95° (c) 120° (d) 155°
11. 11.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 125° (b) 105° (c) 55° (d) 130°
12. 12.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 15° (d) 30°
13. 13.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 145° (d) 120°
14. 14.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 320° (c) 40° (d) 140°
15. 15.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 150° (b) 30° (c) 55° (d) 155°
16. 16.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 95° (b) 140° (c) 85° (d) 135°
17. 17.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 145° (b) 270° (c) 125° (d) 90°
18. 18.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 115° (c) 50° (d) 65°
19. 19.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 55° (c) 140° (d) 125°
20. 20.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) 55° (c) 145° (d) 35°
21. 21.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 65° (c) 25° (d) 115°
22. 22.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 125° (b) 155° (c) 150° (d) 55°
23. 23.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 10° (c) 80° (d) 50°
24. 24.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 70° (c) 110° (d) 145°
25. 25.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 120° (c) 30° (d) 150°
26. 26.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 90° (b) 170° (c) 10° (d) 100°
27. 27.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 120° (c) 140° (d) 100°
28. 28.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 80° (c) 160° (d) 20°
29. 29.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 75° (d) 145°
30. 30.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 11° (c) 20° (d) 10°
31. 31.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 81° (b) 260° (c) 100° (d) 80°
32. 32.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°
33. 33.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 100° (b) 200° (c) 160° (d) 20°
34. 34.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 70° (c) 110° (d) 71°
35. 35.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 95° (d) 120°
36. 36.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 115° (b) 150° (c) 95° (d) 30°
37. 37.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 110° (c) 70° (d) 40°
38. 38.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 55° (b) 130° (c) 125° (d) 105°
39. 39.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 120° (c) 30° (d) 300°
40. 40.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) 70° (c) 160° (d) 340°

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