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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 386 · 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 40° and 70°. What is the third angle? (a) 250° (b) 70° (c) 140° (d) 110°
  2. 2.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 115° (b) 45° (c) 110° (d) 135°
  3. 3.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 150° (d) 160°
  4. 4.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 140° (b) 135° (c) 40° (d) 85°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 280° (c) 40° (d) 140°
  6. 6.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 160° (c) 20° (d) 200°
  7. 7.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 145° (b) 105° (c) 110° (d) 70°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 140° (c) 40° (d) 70°
  9. 9.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 35° (b) 100° (c) 145° (d) 115°
  10. 10.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 130° (b) 80° (c) 150° (d) 50°
  11. 11.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 70° (b) 110° (c) 130° (d) 160°
  12. 12.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) 75° (d) 30°
  13. 13.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 70° (d) 160°
  14. 14.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 40° (d) 100°
  15. 15.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 135° (b) 105° (c) 120° (d) 75°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 56° (c) 125° (d) 55°
  17. 17.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) 80° (d) 81°
  18. 18.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 60° (c) 105° (d) 120°
  19. 19.Two angles of a triangle are 30° and 85°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 150° (d) 95°
  20. 20.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 115° (b) 80° (c) 145° (d) 100°
  21. 21.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 100° (c) 140° (d) 40°
  22. 22.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 150° (b) 20° (c) 50° (d) 160°
  23. 23.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 70° (b) 250° (c) 110° (d) 140°
  24. 24.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 100° (c) 20° (d) 80°
  25. 25.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 70° (c) 35° (d) 125°
  26. 26.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 30° (b) 115° (c) 150° (d) 95°
  27. 27.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 30° (b) 110° (c) 150° (d) 100°
  28. 28.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 100° (c) 80° (d) 155°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 30° (c) 60° (d) 120°
  30. 30.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 105° (b) 110° (c) 35° (d) 145°
  31. 31.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) 255° (d) 75°
  32. 32.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 230° (c) 130° (d) 50°
  33. 33.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 140° (b) 75° (c) 145° (d) 105°
  34. 34.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 105° (d) 125°
  35. 35.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 145° (b) 70° (c) 215° (d) 35°
  36. 36.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 225° (b) 45° (c) 135° (d) 90°
  37. 37.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 160° (d) 80°
  38. 38.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 80° (c) 150° (d) 100°
  39. 39.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 120° (d) 30°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 70° (c) 35° (d) 45°

Answer key

  1. 70°
  2. 135°
  3. 50°
  4. 140°
  5. 140°
  6. 20°
  7. 70°
  8. 70°
  9. 35°
  10. 50°
  11. 110°
  12. 105°
  13. 70°
  14. 140°
  15. 105°
  16. 55°
  17. 80°
  18. 120°
  19. 115°
  20. 80°
  21. 100°
  22. 20°
  23. 70°
  24. 20°
  25. 70°
  26. 150°
  27. 150°
  28. 100°
  29. 60°
  30. 35°
  31. 75°
  32. 50°
  33. 105°
  34. 130°
  35. 145°
  36. 45°
  37. 120°
  38. 80°
  39. 60°
  40. 35°

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