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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 174 · 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 30° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 140° (d) 150°
  2. 2.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 130° (b) 80° (c) 150° (d) 100°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 40° (c) 70° (d) 140°
  4. 4.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 110° (c) 70° (d) 250°
  5. 5.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 60° (b) 110° (c) 120° (d) 130°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 25° (c) 50° (d) 35°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 90° (c) 45° (d) 46°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 150° (c) 30° (d) 75°
  9. 9.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 110° (b) 120° (c) 50° (d) 130°
  10. 10.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 105° (b) 60° (c) 120° (d) 135°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 10° (c) 20° (d) 11°
  12. 12.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 110° (d) 145°
  13. 13.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 15° (c) 16° (d) 165°
  14. 14.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 105° (b) 115° (c) 40° (d) 140°
  15. 15.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 40° (b) 140° (c) 120° (d) 100°
  16. 16.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) 150° (c) 330° (d) 30°
  17. 17.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 125° (b) 45° (c) 100° (d) 135°
  18. 18.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 45° (b) 130° (c) 135° (d) 95°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 30° (d) 40°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 160° (c) 20° (d) 140°
  21. 21.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 150° (b) 155° (c) 55° (d) 125°
  22. 22.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 145° (d) 75°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 150° (d) 300°
  24. 24.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) 40° (d) 140°
  25. 25.Two angles of a triangle are 25° and 100°. What is the exterior angle at the third corner? (a) 55° (b) 155° (c) 125° (d) 80°
  26. 26.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 120° (c) 60° (d) 30°
  27. 27.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 140° (d) 40°
  28. 28.Two angles of a triangle are 30° and 70°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 110° (d) 150°
  29. 29.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 125° (b) 160° (c) 145° (d) 55°
  30. 30.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 55° (b) 130° (c) 105° (d) 125°
  31. 31.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 95° (c) 155° (d) 85°
  32. 32.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°
  33. 33.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 250° (b) 110° (c) 70° (d) 140°
  34. 34.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 145° (b) 55° (c) 160° (d) 35°
  35. 35.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 105° (b) 15° (c) 75° (d) 285°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 41° (c) 80° (d) 40°
  37. 37.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 100° (b) 90° (c) 10° (d) 170°
  38. 38.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 125° (c) 105° (d) 55°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 60° (b) 59° (c) 120° (d) 61°
  40. 40.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 75° (b) 155° (c) 105° (d) 100°

Answer key

  1. 70°
  2. 100°
  3. 70°
  4. 110°
  5. 60°
  6. 25°
  7. 45°
  8. 75°
  9. 50°
  10. 120°
  11. 10°
  12. 110°
  13. 15°
  14. 40°
  15. 40°
  16. 150°
  17. 45°
  18. 135°
  19. 30°
  20. 160°
  21. 125°
  22. 75°
  23. 150°
  24. 40°
  25. 125°
  26. 120°
  27. 100°
  28. 100°
  29. 125°
  30. 55°
  31. 85°
  32. 80°
  33. 70°
  34. 35°
  35. 105°
  36. 40°
  37. 10°
  38. 125°
  39. 60°
  40. 105°

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