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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 530 · 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. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 70° (c) 125° (d) 250°
  2. 2.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) 110° (c) 250° (d) 71°
  3. 3.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 160° (b) 20° (c) 115° (d) 85°
  4. 4.Two angles of a triangle are 25° and 75°. What is the third angle? (a) 80° (b) 105° (c) 100° (d) 155°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 155° (b) 26° (c) 25° (d) 50°
  6. 6.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 155° (b) 80° (c) 125° (d) 100°
  7. 7.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°
  8. 8.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 80° (c) 100° (d) 155°
  9. 9.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 140° (d) 145°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 121° (c) 240° (d) 120°
  11. 11.Two angles of a triangle are 55° and 105°. What is the third angle? (a) 20° (b) 125° (c) 160° (d) 75°
  12. 12.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 270° (b) 110° (c) 90° (d) 160°
  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 straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 66° (c) 115° (d) 130°
  15. 15.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 55° (d) 125°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 150° (c) 75° (d) 30°
  17. 17.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 335° (c) 155° (d) 65°
  18. 18.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 110° (b) 85° (c) 95° (d) 155°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 130° (c) 50° (d) 65°
  20. 20.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 110° (d) 70°
  21. 21.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 91° (b) 135° (c) 90° (d) 270°
  22. 22.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 10° (d) 85°
  23. 23.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 115° (b) 120° (c) 125° (d) 60°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 35° (c) 70° (d) 45°
  25. 25.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 120° (b) 55° (c) 125° (d) 115°
  26. 26.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 80° (d) 145°
  27. 27.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 140° (b) 70° (c) 40° (d) 150°
  28. 28.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 75° (d) 150°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 10° (c) 80° (d) 100°
  30. 30.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 60° (b) 240° (c) 61° (d) 120°
  31. 31.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 155° (b) 55° (c) 150° (d) 125°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 59° (c) 60° (d) 61°
  33. 33.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 80° (b) 125° (c) 100° (d) 135°
  34. 34.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 270° (d) 150°
  35. 35.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 145° (c) 120° (d) 60°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 45° (c) 46° (d) 90°
  37. 37.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 120° (d) 30°
  38. 38.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 110° (b) 235° (c) 55° (d) 125°
  39. 39.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 100° (b) 80° (c) 145° (d) 115°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 25° (c) 150° (d) 15°

Answer key

  1. 125°
  2. 70°
  3. 20°
  4. 80°
  5. 25°
  6. 100°
  7. 120°
  8. 100°
  9. 75°
  10. 120°
  11. 20°
  12. 90°
  13. 60°
  14. 65°
  15. 125°
  16. 75°
  17. 155°
  18. 95°
  19. 65°
  20. 40°
  21. 90°
  22. 10°
  23. 60°
  24. 35°
  25. 125°
  26. 80°
  27. 40°
  28. 75°
  29. 50°
  30. 60°
  31. 55°
  32. 60°
  33. 100°
  34. 90°
  35. 120°
  36. 45°
  37. 60°
  38. 55°
  39. 80°
  40. 15°

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