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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 38 · 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 155°. What is the angle next to it on the same straight line? (a) 26° (b) 155° (c) 25° (d) 205°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 105° (c) 75° (d) 210°
  3. 3.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) 150° (d) 330°
  4. 4.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 65° (c) 130° (d) 25°
  5. 5.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 110° (b) 160° (c) 20° (d) 90°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 121° (c) 120° (d) 240°
  7. 7.Two angles of a triangle are 25° and 60°. What is the third angle? (a) 95° (b) 85° (c) 120° (d) 155°
  8. 8.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 110° (d) 115°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 15° (c) 30° (d) 165°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 110° (b) 40° (c) 70° (d) 220°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 150° (c) 30° (d) 60°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 65° (c) 115° (d) 50°
  13. 13.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 50° (b) 150° (c) 160° (d) 130°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 70° (c) 140° (d) 71°
  15. 15.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 160° (c) 75° (d) 105°
  16. 16.Two angles of a triangle are 25° and 130°. What is the third angle? (a) 25° (b) 205° (c) 155° (d) 50°
  17. 17.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 70° (b) 250° (c) 140° (d) 110°
  18. 18.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 130° (c) 51° (d) 50°
  19. 19.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 65° (d) 115°
  20. 20.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 70° (b) 105° (c) 145° (d) 110°
  21. 21.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 110° (c) 145° (d) 55°
  22. 22.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 145° (b) 100° (c) 35° (d) 115°
  23. 23.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 100° (d) 125°
  24. 24.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 90° (b) 60° (c) 150° (d) 120°
  25. 25.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 115° (b) 65° (c) 245° (d) 130°
  26. 26.Two angles of a triangle are 20° and 115°. What is the third angle? (a) 45° (b) 135° (c) 65° (d) 160°
  27. 27.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 170° (b) 130° (c) 60° (d) 10°
  28. 28.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 20° (b) 65° (c) 160° (d) 135°
  29. 29.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 150° (b) 170° (c) 40° (d) 10°
  30. 30.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 120° (b) 300° (c) 30° (d) 60°
  31. 31.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 125° (b) 115° (c) 55° (d) 120°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 85° (c) 86° (d) 170°
  33. 33.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 140° (d) 60°
  34. 34.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 160° (b) 120° (c) 60° (d) 140°
  35. 35.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 135° (b) 75° (c) 150° (d) 105°
  36. 36.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 220° (b) 140° (c) 80° (d) 40°
  37. 37.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 100° (b) 80° (c) 115° (d) 145°
  38. 38.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 145° (b) 135° (c) 80° (d) 100°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 60° (d) 70°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 50° (c) 155° (d) 25°

Answer key

  1. 25°
  2. 105°
  3. 150°
  4. 130°
  5. 20°
  6. 120°
  7. 95°
  8. 135°
  9. 15°
  10. 110°
  11. 30°
  12. 115°
  13. 130°
  14. 70°
  15. 105°
  16. 25°
  17. 70°
  18. 50°
  19. 115°
  20. 70°
  21. 110°
  22. 35°
  23. 135°
  24. 60°
  25. 65°
  26. 45°
  27. 10°
  28. 20°
  29. 10°
  30. 120°
  31. 125°
  32. 85°
  33. 120°
  34. 120°
  35. 75°
  36. 40°
  37. 80°
  38. 100°
  39. 60°
  40. 25°

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