Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 610 · 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. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 260° (c) 80° (d) 130°
2. 2.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 30° (d) 105°
3. 3.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 50° (c) 115° (d) 25°
4. 4.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 40° (d) 115°
5. 5.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) 25° (d) 150°
6. 6.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 110° (d) 145°
7. 7.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 35° (c) 45° (d) 110°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 71° (c) 70° (d) 110°
9. 9.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 80° (c) 20° (d) 10°
10. 10.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 65° (d) 115°
11. 11.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 90° (c) 150° (d) 270°
12. 12.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 320° (b) 40° (c) 160° (d) 140°
13. 13.Two angles of a triangle are 40° and 80°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 140° (d) 60°
14. 14.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 95° (b) 120° (c) 35° (d) 145°
15. 15.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 110° (c) 220° (d) 70°
16. 16.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 160° (b) 55° (c) 145° (d) 125°
17. 17.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 60° (d) 75°
18. 18.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 270° (b) 150° (c) 120° (d) 90°
19. 19.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 160° (b) 85° (c) 115° (d) 65°
20. 20.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 80° (c) 40° (d) 41°
21. 21.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 85° (d) 10°
22. 22.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 165° (c) 195° (d) 15°
23. 23.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°
24. 24.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°
25. 25.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 260° (b) 100° (c) 80° (d) 160°
26. 26.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 190° (c) 10° (d) 170°
27. 27.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 335° (c) 65° (d) 155°
28. 28.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 80° (c) 100° (d) 10°
29. 29.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 50° (c) 130° (d) 25°
30. 30.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 80° (d) 100°
31. 31.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 210° (b) 30° (c) 105° (d) 150°
32. 32.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 110° (b) 10° (c) 80° (d) 170°
33. 33.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 140° (d) 280°
34. 34.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 70° (c) 160° (d) 20°
35. 35.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 130° (c) 50° (d) 310°
36. 36.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) 305° (c) 35° (d) 125°
37. 37.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 55° (c) 110° (d) 70°
38. 38.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 140° (b) 10° (c) 170° (d) 50°
39. 39.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) 265° (c) 86° (d) 95°
40. 40.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 125° (b) 150° (c) 85° (d) 95°

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