Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 170 · 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) 100° (b) 80° (c) 280° (d) 10°
2. 2.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 145° (c) 55° (d) 110°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 70° (c) 220° (d) 110°
4. 4.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 150° (d) 120°
5. 5.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 86° (c) 265° (d) 95°
6. 6.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 110° (d) 70°
7. 7.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 80° (d) 20°
8. 8.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 115° (b) 155° (c) 270° (d) 90°
9. 9.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 16° (c) 165° (d) 30°
10. 10.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 65° (b) 115° (c) 135° (d) 160°
11. 11.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 20° (c) 80° (d) 100°
12. 12.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 45° (b) 145° (c) 170° (d) 10°
13. 13.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 155° (c) 130° (d) 50°
14. 14.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 90° (c) 55° (d) 45°
15. 15.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 95° (c) 5° (d) 10°
16. 16.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 310° (c) 130° (d) 50°
17. 17.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 110° (b) 70° (c) 95° (d) 155°
18. 18.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 26° (d) 205°
19. 19.Two angles of a triangle are 45° and 65°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 115° (d) 70°
20. 20.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 125° (b) 155° (c) 150° (d) 55°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 140° (b) 40° (c) 100° (d) 280°
22. 22.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 155° (b) 70° (c) 45° (d) 135°
23. 23.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 60° (c) 75° (d) 150°
24. 24.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 90° (b) 270° (c) 150° (d) 120°
25. 25.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 110° (c) 20° (d) 70°
26. 26.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 20° (c) 21° (d) 40°
27. 27.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) 51° (c) 50° (d) 130°
28. 28.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 40° (b) 140° (c) 110° (d) 220°
29. 29.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 155° (c) 25° (d) 65°
30. 30.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 100° (b) 140° (c) 120° (d) 60°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 30° (b) 60° (c) 31° (d) 150°
32. 32.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 10° (c) 160° (d) 20°
33. 33.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 290° (b) 70° (c) 145° (d) 110°
34. 34.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 125° (c) 55° (d) 150°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 85° (c) 170° (d) 95°
36. 36.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 50° (b) 100° (c) 230° (d) 130°
37. 37.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 70° (b) 135° (c) 155° (d) 110°
38. 38.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 85° (b) 115° (c) 95° (d) 160°
39. 39.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 40° (b) 85° (c) 140° (d) 135°
40. 40.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 135° (b) 85° (c) 40° (d) 140°

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