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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 227 · 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 25° and 100°. What is the third angle? (a) 155° (b) 125° (c) 55° (d) 80°
  2. 2.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 90° (b) 10° (c) 170° (d) 100°
  3. 3.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 95° (c) 85° (d) 135°
  4. 4.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 155° (d) 60°
  5. 5.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 35° (c) 145° (d) 36°
  6. 6.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 120° (b) 65° (c) 115° (d) 125°
  7. 7.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 80° (b) 150° (c) 100° (d) 130°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 80° (c) 40° (d) 41°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 240° (c) 121° (d) 120°
  10. 10.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 55° (b) 120° (c) 115° (d) 125°
  11. 11.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 115° (d) 145°
  12. 12.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 50° (c) 40° (d) 100°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 120° (c) 30° (d) 60°
  14. 14.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 125° (d) 90°
  15. 15.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 315° (c) 135° (d) 136°
  16. 16.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 70° (d) 160°
  17. 17.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 120° (b) 130° (c) 60° (d) 110°
  18. 18.Two angles of a triangle are 45° and 100°. What is the third angle? (a) 145° (b) 80° (c) 135° (d) 35°
  19. 19.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 100° (d) 75°
  20. 20.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°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 50° (d) 70°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 115° (b) 130° (c) 66° (d) 65°
  23. 23.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 115° (b) 70° (c) 110° (d) 135°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 130° (d) 65°
  25. 25.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 150° (b) 45° (c) 75° (d) 135°
  26. 26.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) 105° (d) 75°
  27. 27.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 130° (b) 155° (c) 105° (d) 75°
  28. 28.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 70° (c) 150° (d) 110°
  29. 29.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 40° (c) 130° (d) 80°
  30. 30.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 150° (b) 140° (c) 70° (d) 110°
  31. 31.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 80° (b) 15° (c) 165° (d) 115°
  32. 32.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 120° (b) 70° (c) 130° (d) 110°
  33. 33.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 340° (c) 160° (d) 70°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 160° (c) 140° (d) 320°
  35. 35.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 65° (d) 155°
  36. 36.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 105° (b) 170° (c) 85° (d) 10°
  37. 37.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 145° (c) 35° (d) 115°
  38. 38.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 320° (b) 140° (c) 160° (d) 40°
  39. 39.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 65° (c) 35° (d) 145°
  40. 40.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 50° (c) 65° (d) 115°

Answer key

  1. 55°
  2. 10°
  3. 95°
  4. 60°
  5. 35°
  6. 65°
  7. 100°
  8. 40°
  9. 120°
  10. 125°
  11. 100°
  12. 100°
  13. 30°
  14. 145°
  15. 135°
  16. 70°
  17. 60°
  18. 35°
  19. 105°
  20. 120°
  21. 70°
  22. 65°
  23. 70°
  24. 65°
  25. 45°
  26. 75°
  27. 105°
  28. 110°
  29. 80°
  30. 70°
  31. 15°
  32. 110°
  33. 160°
  34. 160°
  35. 130°
  36. 10°
  37. 145°
  38. 40°
  39. 145°
  40. 50°

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