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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 124 · 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 45° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 135° (c) 140° (d) 40°
  2. 2.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) 70° (c) 110° (d) 20°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 75° (b) 76° (c) 150° (d) 105°
  4. 4.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 170° (b) 11° (c) 190° (d) 10°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 40° (d) 70°
  6. 6.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 155° (b) 25° (c) 75° (d) 130°
  7. 7.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°
  8. 8.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 55° (b) 35° (c) 145° (d) 160°
  9. 9.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 61° (b) 240° (c) 60° (d) 120°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 55° (c) 250° (d) 125°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 60° (c) 59° (d) 61°
  12. 12.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 165° (c) 195° (d) 16°
  13. 13.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 160° (b) 20° (c) 120° (d) 80°
  14. 14.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 160° (b) 80° (c) 100° (d) 120°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 145° (b) 35° (c) 36° (d) 70°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 80° (c) 70° (d) 160°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 10° (d) 160°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 100° (d) 50°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 150° (c) 30° (d) 300°
  20. 20.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 120° (b) 50° (c) 110° (d) 130°
  21. 21.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 100° (b) 230° (c) 50° (d) 130°
  22. 22.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 45° (c) 135° (d) 91°
  23. 23.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 120° (b) 85° (c) 25° (d) 155°
  24. 24.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 100° (b) 110° (c) 30° (d) 150°
  25. 25.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 220° (c) 140° (d) 41°
  26. 26.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 50° (b) 130° (c) 51° (d) 230°
  27. 27.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 325° (d) 55°
  28. 28.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 135° (d) 45°
  29. 29.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 155° (b) 60° (c) 145° (d) 120°
  30. 30.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 110° (c) 135° (d) 45°
  31. 31.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 155° (b) 140° (c) 40° (d) 65°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 45° (c) 70° (d) 35°
  33. 33.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 150° (b) 110° (c) 70° (d) 100°
  34. 34.Two angles of a triangle are 40° and 110°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 140° (d) 70°
  35. 35.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 110° (b) 160° (c) 270° (d) 90°
  36. 36.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 235° (b) 110° (c) 55° (d) 125°
  37. 37.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 115° (b) 155° (c) 90° (d) 270°
  38. 38.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 135° (b) 70° (c) 155° (d) 45°
  39. 39.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 80° (b) 100° (c) 145° (d) 115°
  40. 40.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 100° (b) 105° (c) 25° (d) 155°

Answer key

  1. 140°
  2. 110°
  3. 75°
  4. 10°
  5. 70°
  6. 25°
  7. 60°
  8. 145°
  9. 60°
  10. 125°
  11. 60°
  12. 15°
  13. 20°
  14. 100°
  15. 35°
  16. 80°
  17. 10°
  18. 40°
  19. 150°
  20. 50°
  21. 50°
  22. 90°
  23. 25°
  24. 30°
  25. 40°
  26. 50°
  27. 145°
  28. 135°
  29. 120°
  30. 135°
  31. 140°
  32. 35°
  33. 70°
  34. 150°
  35. 90°
  36. 55°
  37. 90°
  38. 45°
  39. 80°
  40. 25°

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