Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 798 · 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 80°. What is the angle next to it on the same straight line? (a) 280° (b) 100° (c) 80° (d) 10°
2. 2.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 130° (b) 85° (c) 95° (d) 145°
3. 3.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 55° (b) 115° (c) 125° (d) 120°
4. 4.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 61°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 86° (c) 95° (d) 85°
6. 6.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 200° (b) 100° (c) 160° (d) 20°
7. 7.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 140° (c) 280° (d) 40°
8. 8.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 150° (d) 80°
9. 9.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 140° (b) 95° (c) 85° (d) 125°
10. 10.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 85° (b) 160° (c) 65° (d) 115°
11. 11.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 40° (d) 65°
12. 12.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 105° (b) 165° (c) 90° (d) 15°
13. 13.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 160° (c) 140° (d) 20°
14. 14.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 110° (b) 125° (c) 55° (d) 235°
15. 15.Two angles of a triangle are 40° and 50°. What is the exterior angle at the third corner? (a) 140° (b) 270° (c) 130° (d) 90°
16. 16.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 155° (b) 85° (c) 95° (d) 110°
17. 17.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 160° (c) 135° (d) 115°
18. 18.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 115° (b) 120° (c) 65° (d) 125°
19. 19.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 50°
20. 20.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 100° (b) 80° (c) 200° (d) 20°
21. 21.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 35° (d) 25°
22. 22.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 95° (b) 160° (c) 115° (d) 85°
23. 23.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 36° (b) 35° (c) 215° (d) 145°
24. 24.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 310° (c) 155° (d) 130°
25. 25.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 40° (d) 70°
26. 26.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 110° (c) 55° (d) 145°
27. 27.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 125° (c) 75° (d) 160°
28. 28.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 70° (c) 55° (d) 35°
29. 29.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 155° (b) 30° (c) 150° (d) 55°
30. 30.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 95° (b) 160° (c) 20° (d) 105°
31. 31.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 95° (b) 125° (c) 140° (d) 85°
32. 32.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 100° (b) 140° (c) 120° (d) 60°
33. 33.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 30° (c) 60° (d) 120°
34. 34.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 110° (b) 70° (c) 250° (d) 125°
35. 35.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 45° (b) 80° (c) 135° (d) 145°
36. 36.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 50° (b) 310° (c) 155° (d) 130°
37. 37.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 26° (b) 205° (c) 155° (d) 25°
38. 38.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 100° (d) 80°
39. 39.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 110° (b) 70° (c) 20° (d) 290°
40. 40.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 55° (b) 120° (c) 125° (d) 115°

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