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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 180 · 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 35° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 150° (c) 65° (d) 145°
  2. 2.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 120° (d) 60°
  3. 3.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 260° (b) 130° (c) 80° (d) 100°
  4. 4.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 60° (b) 150° (c) 120° (d) 90°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 300° (c) 150° (d) 30°
  6. 6.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 130° (b) 160° (c) 70° (d) 50°
  7. 7.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 75° (d) 145°
  8. 8.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 110° (b) 120° (c) 130° (d) 50°
  9. 9.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 125° (b) 105° (c) 75° (d) 130°
  10. 10.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 150° (b) 75° (c) 255° (d) 105°
  11. 11.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 125° (d) 155°
  12. 12.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 130° (b) 85° (c) 145° (d) 95°
  13. 13.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 150° (d) 105°
  14. 14.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°
  15. 15.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 125° (b) 85° (c) 95° (d) 140°
  16. 16.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 40° (c) 140° (d) 100°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 115° (c) 130° (d) 65°
  18. 18.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 90° (c) 135° (d) 91°
  19. 19.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 130° (d) 150°
  20. 20.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 40° (d) 130°
  21. 21.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 70° (c) 40° (d) 20°
  22. 22.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 40° (b) 20° (c) 160° (d) 200°
  23. 23.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 30° (c) 150° (d) 210°
  24. 24.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 70° (c) 110° (d) 71°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 100° (d) 50°
  26. 26.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 80° (b) 110° (c) 170° (d) 10°
  27. 27.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 230° (b) 50° (c) 115° (d) 130°
  28. 28.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 45° (b) 105° (c) 120° (d) 135°
  29. 29.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 65° (c) 66° (d) 115°
  30. 30.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 280° (d) 140°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 130° (c) 25° (d) 155°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 70° (c) 20° (d) 110°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 30° (c) 120° (d) 60°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 20° (c) 160° (d) 140°
  35. 35.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 150°
  36. 36.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 125° (b) 120° (c) 115° (d) 55°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 70° (d) 50°
  38. 38.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 115° (c) 150° (d) 30°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 150° (c) 105° (d) 75°
  40. 40.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 285° (c) 15° (d) 105°

Answer key

  1. 65°
  2. 120°
  3. 80°
  4. 60°
  5. 150°
  6. 50°
  7. 75°
  8. 50°
  9. 75°
  10. 75°
  11. 80°
  12. 85°
  13. 75°
  14. 60°
  15. 95°
  16. 140°
  17. 65°
  18. 90°
  19. 80°
  20. 80°
  21. 40°
  22. 20°
  23. 150°
  24. 70°
  25. 40°
  26. 10°
  27. 50°
  28. 135°
  29. 65°
  30. 80°
  31. 155°
  32. 55°
  33. 30°
  34. 160°
  35. 120°
  36. 125°
  37. 70°
  38. 150°
  39. 75°
  40. 105°

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