Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 300 · 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 25° each. What is the third angle? (a) 65° (b) 155° (c) 130° (d) 25°
2. 2.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 75° (b) 255° (c) 150° (d) 105°
3. 3.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 160° (b) 80° (c) 260° (d) 100°
4. 4.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 15° (c) 150° (d) 25°
5. 5.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 115° (b) 60° (c) 120° (d) 125°
6. 6.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 95° (c) 86° (d) 85°
7. 7.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 45° (c) 115° (d) 135°
8. 8.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 76° (b) 105° (c) 75° (d) 255°
9. 9.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 65° (c) 25° (d) 335°
10. 10.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 160° (d) 145°
11. 11.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 25° (c) 65° (d) 115°
12. 12.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 90° (b) 145° (c) 55° (d) 125°
13. 13.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 120° (c) 140° (d) 60°
14. 14.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 15° (b) 80° (c) 165° (d) 115°
15. 15.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 125° (b) 155° (c) 55° (d) 80°
16. 16.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 130° (c) 25° (d) 310°
17. 17.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 135° (b) 35° (c) 145° (d) 80°
18. 18.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 120° (c) 59° (d) 60°
19. 19.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 80° (b) 150° (c) 100° (d) 130°
20. 20.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 160° (c) 80° (d) 20°
21. 21.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 40° (c) 140° (d) 41°
22. 22.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 270° (b) 155° (c) 115° (d) 90°
23. 23.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 65° (c) 115° (d) 160°
24. 24.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°
25. 25.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 100° (c) 125° (d) 135°
26. 26.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 55° (c) 46° (d) 45°
27. 27.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 30° (c) 150° (d) 100°
28. 28.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 270° (b) 115° (c) 90° (d) 155°
29. 29.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 70° (b) 250° (c) 140° (d) 110°
30. 30.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 110° (c) 35° (d) 145°
31. 31.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 91° (c) 135° (d) 45°
32. 32.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 140° (b) 95° (c) 125° (d) 55°
33. 33.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 85° (d) 150°
34. 34.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 50° (c) 150° (d) 130°
35. 35.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 155° (b) 105° (c) 75° (d) 130°
36. 36.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 95° (c) 85° (d) 150°
37. 37.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 40° (c) 50° (d) 140°
38. 38.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 210° (c) 30° (d) 75°
39. 39.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 45° (c) 160° (d) 135°
40. 40.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 110° (b) 40° (c) 140° (d) 220°

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