Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 901 · 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 angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 70° (c) 45° (d) 35°
2. 2.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 70° (b) 90° (c) 160° (d) 110°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 130° (c) 260° (d) 80°
4. 4.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 130° (b) 80° (c) 50° (d) 150°
5. 5.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 120° (b) 80° (c) 100° (d) 160°
6. 6.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 80° (b) 260° (c) 100° (d) 130°
7. 7.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 290° (c) 70° (d) 145°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 130° (c) 25° (d) 155°
9. 9.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 120° (d) 80°
10. 10.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 40° (c) 130° (d) 310°
11. 11.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 50° (b) 155° (c) 75° (d) 130°
12. 12.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 75° (b) 105° (c) 130° (d) 125°
13. 13.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 150° (b) 95° (c) 85° (d) 115°
14. 14.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 160° (b) 115° (c) 95° (d) 85°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 121° (c) 120° (d) 60°
16. 16.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 145° (b) 125° (c) 160° (d) 55°
17. 17.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 15° (c) 75° (d) 105°
18. 18.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 30° (c) 60° (d) 150°
19. 19.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 135° (c) 45° (d) 91°
20. 20.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 40° (c) 140° (d) 280°
21. 21.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°
22. 22.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 155° (b) 270° (c) 115° (d) 90°
23. 23.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 145° (b) 35° (c) 115° (d) 100°
24. 24.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 115° (b) 150° (c) 145° (d) 65°
25. 25.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 50° (d) 40°
26. 26.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 165° (b) 15° (c) 130° (d) 65°
27. 27.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 130° (d) 50°
28. 28.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 85° (d) 160°
29. 29.Two angles of a triangle are 35° and 100°. What is the third angle? (a) 135° (b) 145° (c) 80° (d) 45°
30. 30.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 130° (d) 65°
31. 31.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 120° (b) 60° (c) 125° (d) 115°
32. 32.Two angles of a triangle are 20° and 120°. What is the exterior angle at the third corner? (a) 160° (b) 60° (c) 140° (d) 40°
33. 33.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 140° (b) 90° (c) 40° (d) 130°
34. 34.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 115° (d) 85°
35. 35.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 40° (c) 140° (d) 50°
36. 36.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 165° (b) 120° (c) 15° (d) 75°
37. 37.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 70° (c) 35° (d) 125°
38. 38.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 125° (c) 100° (d) 135°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 59° (c) 60° (d) 120°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 16° (c) 165° (d) 30°

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