Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 934 · 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 two equal angles are 70° each. What is the third angle? (a) 70° (b) 20° (c) 40° (d) 110°
2. 2.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 20° (b) 160° (c) 45° (d) 155°
3. 3.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 70° (d) 130°
4. 4.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 35° (c) 125° (d) 305°
5. 5.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 25° (d) 130°
6. 6.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 55° (c) 140° (d) 125°
7. 7.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 325° (c) 55° (d) 145°
8. 8.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 250° (b) 140° (c) 70° (d) 110°
9. 9.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) 25° (c) 205° (d) 155°
10. 10.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 145° (c) 35° (d) 110°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 135° (c) 90° (d) 46°
12. 12.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 30° (d) 120°
13. 13.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 40° (c) 140° (d) 320°
14. 14.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 155° (b) 140° (c) 65° (d) 115°
15. 15.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 125° (d) 100°
16. 16.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 110° (c) 70° (d) 135°
17. 17.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 130° (c) 51° (d) 50°
18. 18.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 120° (d) 130°
19. 19.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 80° (c) 100° (d) 81°
20. 20.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 70° (c) 160° (d) 20°
21. 21.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 30° (c) 75° (d) 60°
22. 22.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 240° (c) 121° (d) 120°
23. 23.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 300° (b) 30° (c) 120° (d) 150°
24. 24.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°
25. 25.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 105° (c) 100° (d) 75°
26. 26.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 150° (c) 115° (d) 65°
27. 27.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 115° (c) 90° (d) 270°
28. 28.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 150° (b) 85° (c) 55° (d) 125°
29. 29.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 130° (c) 40° (d) 65°
30. 30.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 110° (b) 60° (c) 130° (d) 120°
31. 31.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 165° (c) 16° (d) 15°
32. 32.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 135° (c) 91° (d) 90°
33. 33.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 60° (c) 61° (d) 120°
34. 34.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 80° (d) 160°
35. 35.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 155° (b) 75° (c) 130° (d) 105°
36. 36.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 70° (c) 45° (d) 110°
37. 37.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 150° (b) 35° (c) 65° (d) 145°
38. 38.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 130° (b) 95° (c) 135° (d) 45°
39. 39.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 5° (b) 95° (c) 275° (d) 85°
40. 40.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 55° (d) 135°

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