Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 906 · 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 80° and 30°. What is the exterior angle at the third corner? (a) 70° (b) 100° (c) 150° (d) 110°
2. 2.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 100° (b) 80° (c) 10° (d) 280°
3. 3.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 50° (c) 100° (d) 10°
4. 4.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 45° (d) 90°
5. 5.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 40° (b) 140° (c) 41° (d) 80°
6. 6.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 160° (d) 115°
7. 7.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 125° (b) 95° (c) 140° (d) 85°
8. 8.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 125° (c) 70° (d) 55°
9. 9.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 120° (d) 105°
10. 10.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 115° (b) 35° (c) 100° (d) 145°
11. 11.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 85° (c) 150° (d) 95°
12. 12.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 210° (c) 31° (d) 30°
13. 13.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 80° (c) 20° (d) 10°
14. 14.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 160° (c) 20° (d) 10°
15. 15.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 140° (b) 270° (c) 90° (d) 130°
16. 16.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 110° (c) 71° (d) 250°
17. 17.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 100° (b) 145° (c) 35° (d) 115°
18. 18.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 100° (b) 160° (c) 120° (d) 80°
19. 19.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 30° (d) 75°
20. 20.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) 65° (d) 50°
21. 21.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 60° (c) 330° (d) 150°
22. 22.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 50° (b) 170° (c) 140° (d) 10°
23. 23.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 130° (b) 115° (c) 230° (d) 50°
24. 24.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 40° (d) 80°
25. 25.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 120° (c) 60° (d) 30°
26. 26.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°
27. 27.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°
28. 28.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 130° (b) 51° (c) 50° (d) 230°
29. 29.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 50° (d) 100°
30. 30.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 90° (c) 270° (d) 155°
31. 31.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 35° (b) 75° (c) 140° (d) 145°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 50° (b) 155° (c) 26° (d) 25°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 20° (c) 100° (d) 200°
34. 34.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 110° (c) 70° (d) 160°
35. 35.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 65° (d) 150°
36. 36.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 155° (b) 25° (c) 90° (d) 115°
37. 37.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°
38. 38.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 135° (b) 115° (c) 65° (d) 160°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 270° (c) 90° (d) 135°
40. 40.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 140° (c) 100° (d) 40°

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