Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 978 · 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 65° and 50°. What is the third angle? (a) 115° (b) 130° (c) 245° (d) 65°
2. 2.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 165° (c) 195° (d) 16°
3. 3.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 130° (b) 230° (c) 100° (d) 50°
4. 4.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 100° (c) 40° (d) 140°
5. 5.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 140° (c) 30° (d) 40°
6. 6.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 135° (b) 70° (c) 155° (d) 25°
7. 7.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 10° (c) 11° (d) 160°
8. 8.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) 280° (c) 100° (d) 10°
9. 9.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 155° (b) 95° (c) 25° (d) 110°
10. 10.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 75° (b) 155° (c) 100° (d) 105°
11. 11.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 120° (c) 60° (d) 40°
12. 12.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 35° (d) 110°
13. 13.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°
14. 14.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 105° (d) 135°
15. 15.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 45° (c) 91° (d) 90°
16. 16.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 105° (b) 160° (c) 95° (d) 20°
17. 17.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°
18. 18.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 20° (b) 21° (c) 160° (d) 40°
19. 19.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 70° (c) 35° (d) 125°
20. 20.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 95° (c) 155° (d) 85°
21. 21.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 50° (d) 65°
22. 22.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 120° (c) 60° (d) 145°
23. 23.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 20° (c) 70° (d) 110°
24. 24.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 80° (b) 100° (c) 105° (d) 155°
25. 25.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 40° (c) 50° (d) 320°
26. 26.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 115° (b) 145° (c) 65° (d) 100°
27. 27.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 100° (c) 10° (d) 80°
28. 28.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 125° (b) 75° (c) 105° (d) 160°
29. 29.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 145° (d) 85°
30. 30.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 55° (c) 325° (d) 145°
31. 31.Two angles of a triangle are 65° and 40°. What is the exterior angle at the third corner? (a) 115° (b) 75° (c) 105° (d) 140°
32. 32.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 150° (d) 85°
33. 33.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 100° (c) 150° (d) 80°
34. 34.Two angles of a triangle are 50° and 95°. What is the third angle? (a) 85° (b) 130° (c) 35° (d) 145°
35. 35.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 20° (c) 70° (d) 110°
36. 36.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 140° (c) 40° (d) 220°
37. 37.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 80° (d) 110°
38. 38.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) 71° (d) 110°
39. 39.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 155° (b) 70° (c) 45° (d) 135°
40. 40.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 50° (c) 130° (d) 51°

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