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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 623 · 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 two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 50° (d) 65°
  2. 2.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 250° (c) 110° (d) 71°
  3. 3.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 130° (b) 140° (c) 90° (d) 50°
  4. 4.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 110° (b) 100° (c) 70° (d) 150°
  5. 5.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) 240° (d) 121°
  6. 6.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 40° (b) 75° (c) 145° (d) 140°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 25° (c) 150° (d) 15°
  8. 8.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 115° (b) 100° (c) 145° (d) 65°
  9. 9.Two angles of a triangle are 45° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 60° (c) 135° (d) 120°
  10. 10.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 140° (b) 85° (c) 125° (d) 95°
  11. 11.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 115° (b) 145° (c) 65° (d) 150°
  12. 12.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 150° (b) 30° (c) 95° (d) 115°
  13. 13.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 85° (c) 95° (d) 160°
  14. 14.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 330° (c) 60° (d) 150°
  15. 15.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 270° (b) 110° (c) 90° (d) 160°
  16. 16.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 165° (b) 115° (c) 80° (d) 15°
  17. 17.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°
  18. 18.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 100° (d) 80°
  19. 19.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 100° (b) 140° (c) 80° (d) 120°
  20. 20.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 55° (c) 56° (d) 125°
  21. 21.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 120° (d) 60°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 140° (c) 50° (d) 40°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 55° (c) 90° (d) 45°
  24. 24.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°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 21° (c) 20° (d) 40°
  26. 26.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 120° (d) 60°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 75° (c) 30° (d) 210°
  28. 28.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 105° (b) 150° (c) 255° (d) 75°
  29. 29.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 140° (b) 125° (c) 55° (d) 95°
  30. 30.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 120° (b) 115° (c) 60° (d) 125°
  31. 31.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 26° (c) 205° (d) 25°
  32. 32.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 85° (c) 130° (d) 95°
  33. 33.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 120° (b) 125° (c) 55° (d) 115°
  34. 34.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) 300° (d) 150°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 95° (c) 86° (d) 85°
  36. 36.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 115° (c) 125° (d) 65°
  37. 37.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 135° (b) 110° (c) 65° (d) 115°
  38. 38.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 130° (c) 90° (d) 270°
  39. 39.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 140° (b) 130° (c) 270° (d) 90°
  40. 40.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 100° (b) 20° (c) 160° (d) 200°

Answer key

  1. 50°
  2. 70°
  3. 130°
  4. 110°
  5. 120°
  6. 140°
  7. 15°
  8. 65°
  9. 120°
  10. 95°
  11. 115°
  12. 150°
  13. 95°
  14. 150°
  15. 90°
  16. 15°
  17. 130°
  18. 100°
  19. 80°
  20. 55°
  21. 120°
  22. 70°
  23. 45°
  24. 80°
  25. 20°
  26. 120°
  27. 105°
  28. 105°
  29. 125°
  30. 120°
  31. 25°
  32. 85°
  33. 55°
  34. 150°
  35. 85°
  36. 115°
  37. 115°
  38. 90°
  39. 90°
  40. 20°

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