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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 195 · 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 straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 70° (c) 160° (d) 20°
  2. 2.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 155° (b) 55° (c) 150° (d) 125°
  3. 3.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) 130° (c) 230° (d) 50°
  4. 4.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 105° (c) 145° (d) 110°
  5. 5.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 135° (c) 40° (d) 140°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 150° (d) 300°
  7. 7.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 125° (d) 75°
  8. 8.Two angles of a triangle are 30° and 85°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 115° (d) 65°
  9. 9.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 130° (c) 40° (d) 50°
  10. 10.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 45° (d) 135°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 50° (c) 100° (d) 80°
  12. 12.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 70° (d) 110°
  13. 13.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 150° (d) 270°
  14. 14.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 160° (b) 135° (c) 20° (d) 65°
  15. 15.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 160° (b) 115° (c) 135° (d) 65°
  16. 16.Two angles of a triangle are 65° and 40°. What is the exterior angle at the third corner? (a) 115° (b) 105° (c) 75° (d) 140°
  17. 17.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 95° (b) 110° (c) 155° (d) 85°
  18. 18.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 15° (b) 165° (c) 105° (d) 90°
  19. 19.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 100° (b) 105° (c) 155° (d) 75°
  20. 20.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 50° (c) 80° (d) 130°
  21. 21.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 145° (c) 110° (d) 55°
  22. 22.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 160° (b) 20° (c) 95° (d) 105°
  23. 23.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 40° (c) 320° (d) 50°
  24. 24.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) 25° (c) 205° (d) 26°
  25. 25.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 110° (c) 40° (d) 70°
  26. 26.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 140° (d) 155°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 20° (c) 100° (d) 80°
  28. 28.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) 60° (c) 30° (d) 120°
  29. 29.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 45° (c) 135° (d) 100°
  30. 30.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°
  31. 31.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 135° (c) 155° (d) 45°
  32. 32.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 105° (b) 120° (c) 135° (d) 75°
  33. 33.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 65° (b) 115° (c) 140° (d) 155°
  34. 34.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 120° (b) 115° (c) 125° (d) 60°
  35. 35.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 120° (b) 100° (c) 80° (d) 140°
  36. 36.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 105° (b) 155° (c) 25° (d) 100°
  37. 37.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 75° (d) 140°
  38. 38.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 260° (b) 100° (c) 130° (d) 80°
  39. 39.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 21° (c) 160° (d) 20°
  40. 40.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 120° (b) 60° (c) 130° (d) 110°

Answer key

  1. 160°
  2. 125°
  3. 50°
  4. 110°
  5. 140°
  6. 150°
  7. 75°
  8. 115°
  9. 130°
  10. 135°
  11. 50°
  12. 110°
  13. 90°
  14. 20°
  15. 115°
  16. 105°
  17. 95°
  18. 15°
  19. 75°
  20. 80°
  21. 110°
  22. 20°
  23. 140°
  24. 25°
  25. 40°
  26. 65°
  27. 100°
  28. 120°
  29. 135°
  30. 70°
  31. 45°
  32. 75°
  33. 115°
  34. 60°
  35. 80°
  36. 25°
  37. 75°
  38. 80°
  39. 20°
  40. 60°

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