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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 267 · 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 45° and 110°. What is the third angle? (a) 70° (b) 25° (c) 155° (d) 135°
  2. 2.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 165° (b) 15° (c) 145° (d) 50°
  3. 3.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 135° (b) 110° (c) 115° (d) 70°
  4. 4.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°
  5. 5.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 100° (b) 145° (c) 80° (d) 115°
  6. 6.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 125° (c) 160° (d) 75°
  7. 7.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 145° (b) 95° (c) 120° (d) 35°
  8. 8.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 200° (c) 160° (d) 21°
  9. 9.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 155° (c) 85° (d) 95°
  10. 10.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 160° (b) 50° (c) 150° (d) 30°
  11. 11.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 135° (b) 85° (c) 140° (d) 95°
  12. 12.Two angles of a triangle are 40° and 70°. What is the exterior angle at the third corner? (a) 140° (b) 70° (c) 110° (d) 250°
  13. 13.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 145° (b) 80° (c) 135° (d) 100°
  14. 14.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 105° (b) 115° (c) 40° (d) 140°
  15. 15.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 90° (b) 270° (c) 150° (d) 120°
  16. 16.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 100° (b) 135° (c) 125° (d) 45°
  17. 17.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 110° (b) 100° (c) 80° (d) 150°
  18. 18.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 120° (b) 60° (c) 240° (d) 61°
  19. 19.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 85° (b) 40° (c) 135° (d) 140°
  20. 20.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 15° (b) 125° (c) 165° (d) 70°
  21. 21.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 160° (b) 85° (c) 105° (d) 95°
  22. 22.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°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 121° (d) 240°
  24. 24.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 110° (b) 20° (c) 70° (d) 290°
  25. 25.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 140° (c) 320° (d) 50°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 60° (c) 150° (d) 30°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 130° (c) 115° (d) 65°
  28. 28.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 160° (c) 100° (d) 260°
  29. 29.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 150° (b) 85° (c) 115° (d) 95°
  30. 30.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 145° (b) 125° (c) 55° (d) 160°
  31. 31.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°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 30° (c) 40° (d) 20°
  33. 33.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 5° (b) 95° (c) 275° (d) 85°
  34. 34.Two angles of a triangle are 45° and 100°. What is the third angle? (a) 145° (b) 80° (c) 135° (d) 35°
  35. 35.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 50°
  36. 36.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 150° (b) 30° (c) 90° (d) 120°
  37. 37.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 100° (c) 10° (d) 80°
  38. 38.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 110° (c) 135° (d) 115°
  39. 39.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 150° (b) 145° (c) 65° (d) 30°
  40. 40.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 75° (b) 155° (c) 105° (d) 100°

Answer key

  1. 25°
  2. 15°
  3. 70°
  4. 80°
  5. 80°
  6. 75°
  7. 35°
  8. 20°
  9. 85°
  10. 150°
  11. 95°
  12. 110°
  13. 100°
  14. 140°
  15. 90°
  16. 45°
  17. 80°
  18. 60°
  19. 40°
  20. 15°
  21. 85°
  22. 150°
  23. 120°
  24. 110°
  25. 140°
  26. 75°
  27. 65°
  28. 100°
  29. 85°
  30. 125°
  31. 80°
  32. 20°
  33. 95°
  34. 35°
  35. 100°
  36. 150°
  37. 20°
  38. 115°
  39. 30°
  40. 75°

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