Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 177 · 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. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 335° (c) 65° (d) 25°
2. 2.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 130° (b) 70° (c) 110° (d) 120°
3. 3.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 31° (c) 150° (d) 210°
4. 4.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 145° (b) 85° (c) 95° (d) 130°
5. 5.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 80° (d) 40°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 66° (c) 115° (d) 130°
7. 7.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 210° (b) 105° (c) 30° (d) 150°
8. 8.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 75° (c) 105° (d) 15°
9. 9.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°
10. 10.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 140° (b) 115° (c) 105° (d) 40°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 20° (c) 11° (d) 10°
12. 12.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 150° (b) 130° (c) 100° (d) 80°
13. 13.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 55° (b) 105° (c) 130° (d) 125°
14. 14.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 155° (b) 26° (c) 50° (d) 25°
15. 15.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 245° (c) 65° (d) 115°
16. 16.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 80° (c) 10° (d) 100°
17. 17.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) 25° (d) 30°
18. 18.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) 160° (d) 11°
19. 19.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 285° (c) 105° (d) 15°
20. 20.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 50° (d) 70°
21. 21.Two angles of a triangle are 60° and 110°. What is the third angle? (a) 170° (b) 70° (c) 120° (d) 10°
22. 22.Two angles of a triangle are 55° and 50°. What is the exterior angle at the third corner? (a) 75° (b) 130° (c) 125° (d) 105°
23. 23.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 125° (b) 130° (c) 105° (d) 75°
24. 24.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) 40° (d) 30°
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) 320° (d) 50°
26. 26.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 135° (b) 155° (c) 160° (d) 45°
27. 27.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 120° (c) 125° (d) 55°
28. 28.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 40° (c) 130° (d) 50°
29. 29.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 115° (c) 65° (d) 25°
30. 30.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 145° (b) 70° (c) 36° (d) 35°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 80° (c) 81° (d) 100°
32. 32.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 80° (d) 70°
33. 33.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 50° (d) 25°
34. 34.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 115° (b) 60° (c) 120° (d) 125°
35. 35.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 160° (b) 85° (c) 105° (d) 95°
36. 36.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 60° (b) 115° (c) 120° (d) 125°
37. 37.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 105° (b) 10° (c) 170° (d) 85°
38. 38.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
39. 39.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 110° (b) 145° (c) 70° (d) 105°
40. 40.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 150° (b) 270° (c) 120° (d) 90°

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