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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 591 · 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 40° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 140° (d) 280°
  2. 2.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 85° (d) 86°
  3. 3.Two angles of a triangle are 20° and 105°. What is the exterior angle at the third corner? (a) 160° (b) 75° (c) 125° (d) 55°
  4. 4.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 100° (b) 10° (c) 280° (d) 80°
  5. 5.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 140° (b) 170° (c) 10° (d) 50°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 140° (d) 50°
  7. 7.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 135° (b) 100° (c) 80° (d) 145°
  8. 8.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 235° (b) 55° (c) 110° (d) 125°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 150° (d) 75°
  10. 10.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 245° (b) 115° (c) 130° (d) 65°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 120° (c) 60° (d) 121°
  12. 12.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 120° (c) 61° (d) 30°
  13. 13.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 125° (b) 55° (c) 305° (d) 35°
  14. 14.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 145° (b) 65° (c) 150° (d) 115°
  15. 15.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 16° (c) 195° (d) 15°
  16. 16.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 115° (b) 160° (c) 85° (d) 65°
  17. 17.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 125° (b) 160° (c) 55° (d) 145°
  18. 18.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 105° (b) 55° (c) 130° (d) 125°
  19. 19.Two angles of a triangle are 40° and 80°. What is the third angle? (a) 140° (b) 60° (c) 120° (d) 100°
  20. 20.Two angles of a triangle are 45° and 120°. What is the third angle? (a) 165° (b) 135° (c) 15° (d) 60°
  21. 21.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 110° (b) 40° (c) 220° (d) 140°
  22. 22.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) 165° (d) 30°
  23. 23.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 40° (d) 50°
  24. 24.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 130° (b) 110° (c) 120° (d) 70°
  25. 25.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) 145° (c) 325° (d) 55°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 140° (c) 20° (d) 160°
  27. 27.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 50° (d) 115°
  28. 28.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 130° (c) 40° (d) 50°
  29. 29.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 50° (b) 130° (c) 155° (d) 310°
  30. 30.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 75° (b) 150° (c) 135° (d) 105°
  31. 31.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 155° (c) 65° (d) 25°
  32. 32.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 150° (d) 75°
  33. 33.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 145° (b) 80° (c) 100° (d) 115°
  34. 34.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 125° (b) 115° (c) 120° (d) 65°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 40° (c) 110° (d) 220°
  36. 36.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 95° (b) 145° (c) 130° (d) 85°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 30° (d) 40°
  38. 38.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 120° (b) 150° (c) 300° (d) 60°
  39. 39.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 160° (b) 140° (c) 60° (d) 20°
  40. 40.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 145° (c) 85° (d) 95°

Answer key

  1. 80°
  2. 85°
  3. 125°
  4. 100°
  5. 10°
  6. 70°
  7. 100°
  8. 55°
  9. 75°
  10. 115°
  11. 120°
  12. 60°
  13. 125°
  14. 115°
  15. 15°
  16. 65°
  17. 125°
  18. 55°
  19. 60°
  20. 15°
  21. 40°
  22. 15°
  23. 100°
  24. 70°
  25. 145°
  26. 160°
  27. 50°
  28. 80°
  29. 130°
  30. 105°
  31. 130°
  32. 135°
  33. 80°
  34. 65°
  35. 110°
  36. 95°
  37. 30°
  38. 60°
  39. 20°
  40. 95°

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