Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 358 · 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.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 35° (d) 70°
2. 2.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 65° (c) 130° (d) 40°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 60° (b) 59° (c) 61° (d) 120°
4. 4.Two angles of a triangle are 45° and 75°. What is the exterior angle at the third corner? (a) 135° (b) 105° (c) 120° (d) 60°
5. 5.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 160° (d) 10°
6. 6.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) 145° (c) 35° (d) 55°
7. 7.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 30° (d) 40°
8. 8.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 290° (c) 110° (d) 20°
9. 9.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 140° (c) 320° (d) 50°
10. 10.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 160° (b) 155° (c) 45° (d) 135°
11. 11.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 60° (c) 120° (d) 140°
12. 12.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 90° (b) 130° (c) 140° (d) 270°
13. 13.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 61° (c) 60° (d) 30°
14. 14.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 55° (b) 125° (c) 115° (d) 120°
15. 15.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 165° (b) 15° (c) 75° (d) 120°
16. 16.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°
17. 17.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 70° (d) 55°
18. 18.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 105° (d) 30°
19. 19.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 155° (b) 150° (c) 55° (d) 125°
20. 20.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 70° (c) 20° (d) 110°
21. 21.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 25° (d) 50°
22. 22.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 160° (b) 55° (c) 125° (d) 145°
23. 23.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 280° (c) 100° (d) 140°
24. 24.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 55° (c) 56° (d) 125°
25. 25.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 110° (c) 71° (d) 70°
26. 26.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 100° (b) 120° (c) 60° (d) 140°
27. 27.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 5° (d) 10°
28. 28.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 75° (b) 100° (c) 105° (d) 155°
29. 29.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 220° (b) 140° (c) 80° (d) 40°
30. 30.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 100° (d) 105°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 220° (c) 110° (d) 40°
32. 32.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 15° (c) 30° (d) 25°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 25° (b) 26° (c) 155° (d) 50°
34. 34.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) 5° (d) 275°
35. 35.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 70° (c) 250° (d) 71°
36. 36.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 105° (b) 100° (c) 155° (d) 80°
37. 37.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 105° (b) 160° (c) 75° (d) 125°
38. 38.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 85° (c) 160° (d) 95°
39. 39.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 135° (b) 105° (c) 150° (d) 75°
40. 40.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 125° (d) 85°

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