Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 37 · 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 30° and 125°. What is the third angle? (a) 150° (b) 55° (c) 25° (d) 155°
2. 2.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 270° (b) 115° (c) 90° (d) 155°
3. 3.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 45° (b) 115° (c) 110° (d) 135°
4. 4.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 25° (c) 50° (d) 35°
5. 5.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 120° (d) 30°
6. 6.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 41° (c) 220° (d) 140°
7. 7.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 150° (b) 140° (c) 40° (d) 70°
8. 8.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 70° (b) 150° (c) 100° (d) 110°
9. 9.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 135° (b) 130° (c) 85° (d) 95°
10. 10.Two angles of a triangle are 45° and 120°. What is the third angle? (a) 165° (b) 60° (c) 15° (d) 135°
11. 11.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 55° (b) 85° (c) 150° (d) 125°
12. 12.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 115° (b) 65° (c) 145° (d) 100°
13. 13.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 55° (b) 110° (c) 125° (d) 235°
14. 14.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 45° (c) 110° (d) 35°
15. 15.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 160° (b) 80° (c) 260° (d) 100°
16. 16.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 70° (d) 290°
17. 17.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°
18. 18.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 90° (c) 270° (d) 150°
19. 19.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 155° (b) 65° (c) 115° (d) 140°
20. 20.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 85° (b) 145° (c) 95° (d) 130°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 20° (c) 160° (d) 140°
22. 22.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 15° (c) 165° (d) 16°
23. 23.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 55° (c) 135° (d) 125°
24. 24.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 85° (b) 15° (c) 165° (d) 110°
25. 25.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°
26. 26.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 80° (c) 40° (d) 140°
27. 27.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 135° (b) 75° (c) 150° (d) 105°
28. 28.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 40° (c) 50° (d) 80°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 95° (c) 86° (d) 170°
30. 30.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 40° (c) 120° (d) 140°
31. 31.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 40° (d) 140°
32. 32.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 155° (d) 25°
33. 33.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 145° (b) 150° (c) 65° (d) 115°
34. 34.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 55° (d) 125°
35. 35.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 280° (c) 80° (d) 100°
36. 36.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 135° (c) 75° (d) 105°
37. 37.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 70° (c) 125° (d) 250°
38. 38.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 55° (d) 110°
39. 39.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 145° (d) 105°
40. 40.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 150° (b) 30° (c) 90° (d) 120°

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