Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 662 · 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 50° and 50°. What is the third angle? (a) 130° (b) 260° (c) 80° (d) 100°
2. 2.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 95° (d) 5°
3. 3.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°
4. 4.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 105° (b) 65° (c) 115° (d) 140°
5. 5.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 160° (b) 100° (c) 120° (d) 80°
6. 6.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 145° (b) 125° (c) 55° (d) 160°
7. 7.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 140° (c) 20° (d) 30°
8. 8.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 60° (b) 160° (c) 120° (d) 140°
9. 9.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 125° (d) 70°
10. 10.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 25° (c) 150° (d) 15°
11. 11.Two angles of a triangle are 30° and 85°. What is the exterior angle at the third corner? (a) 65° (b) 95° (c) 150° (d) 115°
12. 12.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 50° (b) 230° (c) 51° (d) 130°
13. 13.Two angles of a triangle are 25° and 60°. What is the third angle? (a) 95° (b) 155° (c) 120° (d) 85°
14. 14.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 135° (c) 45° (d) 90°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 85° (c) 95° (d) 10°
16. 16.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 100° (b) 80° (c) 260° (d) 160°
17. 17.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 70° (c) 120° (d) 30°
18. 18.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 145° (d) 135°
19. 19.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 25° (c) 26° (d) 155°
20. 20.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 20° (c) 70° (d) 110°
21. 21.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 50° (b) 95° (c) 130° (d) 135°
22. 22.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 35° (c) 145° (d) 90°
23. 23.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 135° (d) 85°
24. 24.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°
25. 25.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 35° (d) 45°
26. 26.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 150° (c) 60° (d) 30°
27. 27.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 110° (d) 55°
28. 28.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 160° (b) 35° (c) 55° (d) 145°
29. 29.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 145° (d) 35°
30. 30.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 130° (c) 50° (d) 40°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 165° (c) 30° (d) 15°
32. 32.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 125° (b) 145° (c) 90° (d) 35°
33. 33.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 11° (c) 10° (d) 160°
34. 34.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 31° (c) 30° (d) 150°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 50° (b) 130° (c) 100° (d) 51°
36. 36.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 105° (d) 70°
37. 37.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°
38. 38.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 115° (b) 125° (c) 120° (d) 55°
39. 39.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 145° (d) 130°
40. 40.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 50° (d) 100°

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