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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 831 · 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 40°. What is the angle next to it on the same straight line? (a) 140° (b) 40° (c) 50° (d) 320°
  2. 2.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 150° (b) 115° (c) 65° (d) 145°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 50° (c) 260° (d) 80°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 60° (c) 30° (d) 150°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 75° (d) 30°
  6. 6.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 76° (c) 75° (d) 105°
  7. 7.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 155° (b) 105° (c) 100° (d) 75°
  8. 8.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 70° (c) 110° (d) 150°
  9. 9.Two angles of a triangle are 50° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 95° (c) 85° (d) 130°
  10. 10.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 125° (b) 75° (c) 160° (d) 105°
  11. 11.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 31° (c) 210° (d) 30°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 160° (c) 20° (d) 10°
  13. 13.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 70° (c) 20° (d) 110°
  14. 14.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 130° (b) 90° (c) 270° (d) 140°
  15. 15.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 120° (c) 145° (d) 95°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 80° (c) 10° (d) 50°
  17. 17.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 105° (b) 120° (c) 45° (d) 135°
  18. 18.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) 60° (c) 300° (d) 30°
  19. 19.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 91° (c) 90° (d) 135°
  20. 20.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 15° (c) 75° (d) 105°
  21. 21.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 125° (b) 120° (c) 65° (d) 115°
  22. 22.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 105° (b) 35° (c) 110° (d) 145°
  23. 23.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°
  24. 24.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 85° (d) 95°
  25. 25.Two angles of a triangle are 45° and 120°. What is the third angle? (a) 135° (b) 60° (c) 165° (d) 15°
  26. 26.Two angles of a triangle are 40° and 95°. What is the exterior angle at the third corner? (a) 135° (b) 140° (c) 85° (d) 45°
  27. 27.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 86° (c) 95° (d) 265°
  28. 28.Two angles of a triangle are 30° and 45°. What is the third angle? (a) 135° (b) 150° (c) 105° (d) 75°
  29. 29.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 140° (b) 100° (c) 80° (d) 280°
  30. 30.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 125° (b) 80° (c) 135° (d) 100°
  31. 31.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 140° (b) 95° (c) 40° (d) 125°
  32. 32.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 100° (c) 140° (d) 50°
  33. 33.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 100° (b) 105° (c) 155° (d) 75°
  34. 34.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 95° (b) 160° (c) 105° (d) 85°
  35. 35.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 135° (d) 45°
  36. 36.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 85° (b) 115° (c) 160° (d) 65°
  37. 37.Two angles of a triangle are 50° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 130° (c) 30° (d) 150°
  38. 38.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°
  39. 39.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 125° (d) 105°
  40. 40.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 140° (c) 60° (d) 120°

Answer key

  1. 140°
  2. 65°
  3. 130°
  4. 30°
  5. 75°
  6. 75°
  7. 75°
  8. 110°
  9. 95°
  10. 105°
  11. 30°
  12. 10°
  13. 40°
  14. 90°
  15. 95°
  16. 50°
  17. 135°
  18. 120°
  19. 90°
  20. 105°
  21. 65°
  22. 35°
  23. 70°
  24. 95°
  25. 15°
  26. 135°
  27. 85°
  28. 105°
  29. 100°
  30. 80°
  31. 40°
  32. 100°
  33. 75°
  34. 85°
  35. 135°
  36. 65°
  37. 150°
  38. 70°
  39. 130°
  40. 60°

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