Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 285 · 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 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 70° (d) 30°
2. 2.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 80° (d) 145°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 100° (b) 130° (c) 51° (d) 50°
4. 4.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 100° (c) 80° (d) 40°
5. 5.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 140° (b) 75° (c) 105° (d) 115°
6. 6.Two angles of a triangle are 40° and 80°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 100° (d) 60°
7. 7.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 125° (b) 90° (c) 145° (d) 55°
8. 8.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 130° (b) 65° (c) 165° (d) 15°
9. 9.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 110° (b) 145° (c) 105° (d) 70°
10. 10.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 315° (c) 136° (d) 135°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 95° (c) 10° (d) 85°
12. 12.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 270° (c) 145° (d) 90°
13. 13.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 40° (c) 140° (d) 80°
14. 14.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 105° (b) 150° (c) 135° (d) 75°
15. 15.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 110° (b) 35° (c) 145° (d) 105°
16. 16.Two angles of a triangle are 45° and 65°. What is the exterior angle at the third corner? (a) 135° (b) 110° (c) 115° (d) 70°
17. 17.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 30° (d) 105°
18. 18.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 80° (b) 145° (c) 115° (d) 100°
19. 19.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 40° (c) 120° (d) 60°
20. 20.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 65° (c) 115° (d) 25°
21. 21.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 95° (b) 150° (c) 65° (d) 115°
22. 22.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 65° (b) 150° (c) 145° (d) 115°
23. 23.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 55° (c) 56° (d) 125°
24. 24.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 110° (b) 145° (c) 290° (d) 70°
25. 25.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 150° (c) 75° (d) 76°
26. 26.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 35° (d) 110°
27. 27.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 40° (c) 50° (d) 130°
28. 28.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°
29. 29.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 45° (b) 115° (c) 135° (d) 110°
30. 30.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 140° (d) 100°
31. 31.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 65° (c) 130° (d) 50°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 125° (c) 56° (d) 55°
33. 33.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 65° (c) 295° (d) 115°
34. 34.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 10° (c) 100° (d) 50°
35. 35.Two angles of a triangle are 25° and 75°. What is the third angle? (a) 100° (b) 80° (c) 155° (d) 105°
36. 36.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 140° (b) 320° (c) 40° (d) 160°
37. 37.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 40° (b) 140° (c) 130° (d) 90°
38. 38.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 100° (b) 110° (c) 150° (d) 30°
39. 39.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 70° (c) 55° (d) 125°
40. 40.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 21° (c) 20° (d) 160°

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