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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 322 · 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 70° and 70°. What is the exterior angle at the third corner? (a) 140° (b) 110° (c) 220° (d) 40°
  2. 2.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 155° (b) 100° (c) 105° (d) 75°
  3. 3.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 136° (c) 135° (d) 45°
  4. 4.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 135° (b) 145° (c) 80° (d) 35°
  5. 5.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 85° (b) 110° (c) 155° (d) 95°
  6. 6.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 65° (b) 140° (c) 105° (d) 115°
  7. 7.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 110° (c) 290° (d) 20°
  8. 8.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 110° (b) 45° (c) 115° (d) 135°
  9. 9.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 55° (c) 145° (d) 325°
  10. 10.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 135° (b) 150° (c) 75° (d) 30°
  11. 11.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 25° (b) 155° (c) 95° (d) 110°
  12. 12.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 50° (b) 150° (c) 80° (d) 130°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 120° (c) 30° (d) 60°
  14. 14.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 105° (d) 70°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 145° (c) 290° (d) 110°
  16. 16.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 10° (c) 100° (d) 20°
  17. 17.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 235° (b) 125° (c) 110° (d) 55°
  18. 18.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 95° (c) 160° (d) 85°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 25° (c) 130° (d) 310°
  20. 20.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 125° (b) 85° (c) 140° (d) 95°
  21. 21.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 125° (d) 105°
  22. 22.Two angles of a triangle are 40° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 140° (c) 30° (d) 150°
  23. 23.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 60° (b) 120° (c) 140° (d) 160°
  24. 24.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 340° (c) 160° (d) 20°
  25. 25.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 120° (b) 125° (c) 65° (d) 115°
  26. 26.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 120° (b) 150° (c) 30° (d) 90°
  27. 27.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 45° (b) 155° (c) 70° (d) 135°
  28. 28.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 120° (b) 140° (c) 80° (d) 100°
  29. 29.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) 30° (c) 120° (d) 60°
  30. 30.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 150° (b) 100° (c) 30° (d) 110°
  31. 31.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 30° (d) 105°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 130° (c) 65° (d) 40°
  33. 33.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 20° (b) 135° (c) 160° (d) 65°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 55° (b) 56° (c) 125° (d) 110°
  35. 35.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 150° (d) 145°
  36. 36.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 70° (b) 130° (c) 160° (d) 110°
  37. 37.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 85° (b) 170° (c) 105° (d) 10°
  38. 38.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 75° (b) 145° (c) 140° (d) 105°
  39. 39.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 155° (b) 115° (c) 90° (d) 25°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 160° (c) 40° (d) 20°

Answer key

  1. 140°
  2. 105°
  3. 135°
  4. 145°
  5. 95°
  6. 65°
  7. 110°
  8. 45°
  9. 145°
  10. 30°
  11. 25°
  12. 130°
  13. 60°
  14. 110°
  15. 145°
  16. 20°
  17. 55°
  18. 95°
  19. 155°
  20. 85°
  21. 130°
  22. 150°
  23. 120°
  24. 160°
  25. 65°
  26. 150°
  27. 135°
  28. 80°
  29. 120°
  30. 30°
  31. 30°
  32. 65°
  33. 20°
  34. 55°
  35. 65°
  36. 70°
  37. 10°
  38. 105°
  39. 25°
  40. 20°

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