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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 794 · 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.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 60° (d) 30°
  2. 2.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 65° (c) 66° (d) 245°
  3. 3.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 150° (b) 75° (c) 30° (d) 135°
  4. 4.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 10° (b) 170° (c) 50° (d) 140°
  5. 5.Two angles of a triangle are 20° and 120°. What is the exterior angle at the third corner? (a) 60° (b) 40° (c) 160° (d) 140°
  6. 6.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 20° (c) 70° (d) 110°
  7. 7.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 75° (b) 105° (c) 125° (d) 130°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 40° (c) 160° (d) 20°
  9. 9.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 115° (d) 120°
  10. 10.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 50° (c) 80° (d) 130°
  11. 11.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 330° (d) 150°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 40° (b) 80° (c) 140° (d) 41°
  13. 13.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 125° (d) 160°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 80° (d) 160°
  15. 15.Two angles of a triangle are 60° and 60°. What is the exterior angle at the third corner? (a) 60° (b) 240° (c) 121° (d) 120°
  16. 16.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 145° (d) 155°
  17. 17.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 100° (b) 160° (c) 120° (d) 80°
  18. 18.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 85° (b) 155° (c) 120° (d) 60°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 290° (c) 110° (d) 145°
  20. 20.Two angles of a triangle are 50° and 100°. What is the third angle? (a) 150° (b) 30° (c) 130° (d) 80°
  21. 21.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 70° (b) 130° (c) 120° (d) 110°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 140° (c) 40° (d) 20°
  23. 23.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 210° (b) 150° (c) 30° (d) 60°
  24. 24.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 70° (b) 110° (c) 135° (d) 115°
  25. 25.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 70° (b) 145° (c) 35° (d) 215°
  26. 26.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 110° (b) 95° (c) 85° (d) 155°
  27. 27.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 150° (d) 255°
  28. 28.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 60° (b) 240° (c) 120° (d) 61°
  29. 29.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 145° (b) 120° (c) 155° (d) 60°
  30. 30.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 100° (b) 160° (c) 260° (d) 80°
  31. 31.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 145° (b) 105° (c) 75° (d) 140°
  32. 32.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) 150° (d) 60°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 150° (b) 30° (c) 300° (d) 120°
  34. 34.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 145° (b) 170° (c) 10° (d) 45°
  35. 35.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 35° (c) 55° (d) 145°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 55° (b) 110° (c) 125° (d) 56°
  37. 37.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 125° (d) 90°
  38. 38.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 140° (b) 70° (c) 150° (d) 110°
  39. 39.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) 60° (d) 30°
  40. 40.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 60° (b) 120° (c) 100° (d) 140°

Answer key

  1. 60°
  2. 65°
  3. 30°
  4. 10°
  5. 140°
  6. 110°
  7. 75°
  8. 20°
  9. 125°
  10. 80°
  11. 150°
  12. 40°
  13. 75°
  14. 80°
  15. 120°
  16. 60°
  17. 80°
  18. 60°
  19. 145°
  20. 30°
  21. 70°
  22. 20°
  23. 150°
  24. 70°
  25. 35°
  26. 95°
  27. 105°
  28. 60°
  29. 120°
  30. 80°
  31. 105°
  32. 75°
  33. 150°
  34. 10°
  35. 145°
  36. 55°
  37. 145°
  38. 110°
  39. 30°
  40. 60°

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