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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 416 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 115° (b) 40° (c) 140° (d) 105°
  2. 2.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 140° (c) 250° (d) 70°
  3. 3.Two angles of a triangle are 25° and 60°. What is the third angle? (a) 120° (b) 95° (c) 155° (d) 85°
  4. 4.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 155° (b) 90° (c) 270° (d) 115°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 120° (c) 30° (d) 60°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 140° (c) 71° (d) 70°
  7. 7.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 40° (b) 115° (c) 105° (d) 140°
  8. 8.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 115° (c) 150° (d) 30°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 150° (c) 300° (d) 120°
  10. 10.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 75° (b) 155° (c) 130° (d) 105°
  11. 11.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 60° (b) 110° (c) 130° (d) 120°
  12. 12.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) 205° (c) 155° (d) 25°
  13. 13.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 150° (c) 120° (d) 30°
  14. 14.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 140° (b) 110° (c) 150° (d) 70°
  15. 15.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 140° (b) 145° (c) 105° (d) 75°
  16. 16.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 45° (b) 130° (c) 95° (d) 135°
  17. 17.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 170° (b) 10° (c) 11° (d) 190°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 10° (c) 80° (d) 100°
  19. 19.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 240° (b) 120° (c) 60° (d) 61°
  20. 20.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 270° (b) 90° (c) 125° (d) 145°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 140° (c) 30° (d) 20°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 45° (d) 35°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 60° (d) 70°
  24. 24.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 95° (d) 5°
  25. 25.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) 125° (d) 35°
  26. 26.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 100° (c) 80° (d) 10°
  27. 27.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 140° (b) 100° (c) 80° (d) 120°
  28. 28.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 65° (b) 155° (c) 140° (d) 115°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 160° (c) 81° (d) 80°
  30. 30.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) 310° (c) 130° (d) 50°
  31. 31.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°
  32. 32.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 115° (b) 25° (c) 65° (d) 295°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 100° (b) 20° (c) 200° (d) 80°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 30° (c) 60° (d) 150°
  35. 35.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 215° (d) 36°
  36. 36.Two angles of a triangle are 50° and 100°. What is the exterior angle at the third corner? (a) 150° (b) 80° (c) 30° (d) 130°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 25° (c) 50° (d) 155°
  38. 38.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 120° (b) 35° (c) 145° (d) 95°
  39. 39.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 110° (d) 145°
  40. 40.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 55° (b) 105° (c) 125° (d) 130°

Answer key

  1. 140°
  2. 110°
  3. 95°
  4. 90°
  5. 30°
  6. 70°
  7. 140°
  8. 150°
  9. 150°
  10. 75°
  11. 120°
  12. 25°
  13. 150°
  14. 70°
  15. 75°
  16. 45°
  17. 10°
  18. 50°
  19. 60°
  20. 90°
  21. 20°
  22. 35°
  23. 60°
  24. 10°
  25. 125°
  26. 20°
  27. 80°
  28. 65°
  29. 80°
  30. 130°
  31. 55°
  32. 115°
  33. 100°
  34. 75°
  35. 35°
  36. 150°
  37. 25°
  38. 35°
  39. 110°
  40. 125°

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