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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 871 · 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 25° and 35°. What is the third angle? (a) 60° (b) 155° (c) 145° (d) 120°
  2. 2.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 320° (b) 40° (c) 140° (d) 160°
  3. 3.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 100° (b) 110° (c) 150° (d) 80°
  4. 4.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 40° (c) 320° (d) 50°
  5. 5.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 100° (b) 145° (c) 135° (d) 80°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 45° (c) 110° (d) 70°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 20° (c) 40° (d) 140°
  8. 8.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 135° (d) 55°
  9. 9.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 120° (b) 95° (c) 155° (d) 85°
  10. 10.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 65° (b) 35° (c) 150° (d) 145°
  11. 11.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°
  12. 12.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 120° (c) 100° (d) 140°
  13. 13.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 135° (b) 145° (c) 100° (d) 80°
  14. 14.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 30° (d) 110°
  15. 15.Two angles of a triangle are 50° and 100°. What is the third angle? (a) 150° (b) 130° (c) 80° (d) 30°
  16. 16.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 40° (c) 140° (d) 100°
  17. 17.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 55° (b) 130° (c) 105° (d) 125°
  18. 18.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 100° (d) 70°
  19. 19.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 135° (b) 125° (c) 80° (d) 100°
  20. 20.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 80° (d) 20°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 300° (c) 30° (d) 150°
  22. 22.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 95° (b) 30° (c) 115° (d) 150°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 40° (d) 70°
  24. 24.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 130° (b) 125° (c) 75° (d) 105°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 11° (c) 20° (d) 10°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 150° (b) 60° (c) 31° (d) 30°
  27. 27.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 145° (d) 80°
  28. 28.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 115° (b) 85° (c) 160° (d) 95°
  29. 29.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 160° (d) 140°
  30. 30.Two angles of a triangle are 55° and 55°. What is the exterior angle at the third corner? (a) 250° (b) 110° (c) 125° (d) 70°
  31. 31.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 120° (b) 160° (c) 60° (d) 140°
  32. 32.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 155° (b) 100° (c) 25° (d) 105°
  33. 33.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 120° (c) 150° (d) 30°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 60° (c) 70° (d) 120°
  35. 35.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 220° (c) 140° (d) 40°
  36. 36.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 50° (d) 65°
  37. 37.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 40° (b) 155° (c) 65° (d) 140°
  38. 38.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) 41° (d) 40°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 55° (c) 70° (d) 250°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 100° (c) 40° (d) 50°

Answer key

  1. 120°
  2. 40°
  3. 80°
  4. 140°
  5. 80°
  6. 35°
  7. 20°
  8. 125°
  9. 95°
  10. 35°
  11. 105°
  12. 100°
  13. 100°
  14. 150°
  15. 30°
  16. 140°
  17. 55°
  18. 110°
  19. 80°
  20. 20°
  21. 150°
  22. 30°
  23. 70°
  24. 75°
  25. 10°
  26. 30°
  27. 100°
  28. 95°
  29. 60°
  30. 110°
  31. 120°
  32. 25°
  33. 120°
  34. 60°
  35. 40°
  36. 50°
  37. 140°
  38. 40°
  39. 125°
  40. 40°

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