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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 569 · 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 30°. What is the third angle? (a) 150° (b) 140° (c) 70° (d) 110°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 30° (c) 40° (d) 20°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 11° (d) 10°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 11° (c) 20° (d) 10°
  5. 5.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) 50° (d) 70°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 145° (b) 35° (c) 36° (d) 70°
  7. 7.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 155° (b) 55° (c) 125° (d) 80°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 45° (c) 46° (d) 55°
  9. 9.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 30° (c) 150° (d) 60°
  10. 10.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 50° (c) 115° (d) 25°
  11. 11.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 120° (b) 30° (c) 90° (d) 150°
  12. 12.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 85° (b) 140° (c) 135° (d) 45°
  13. 13.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 100° (b) 125° (c) 80° (d) 155°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 35° (c) 110° (d) 45°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 160° (d) 80°
  16. 16.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 105° (b) 110° (c) 70° (d) 145°
  17. 17.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 10° (c) 85° (d) 5°
  18. 18.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 80° (d) 145°
  19. 19.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 95° (b) 110° (c) 85° (d) 155°
  20. 20.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 135° (b) 105° (c) 60° (d) 120°
  21. 21.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 60° (b) 125° (c) 115° (d) 120°
  22. 22.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 85° (b) 120° (c) 95° (d) 145°
  23. 23.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) 120° (d) 121°
  24. 24.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 50° (b) 150° (c) 160° (d) 130°
  25. 25.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 150° (b) 160° (c) 30° (d) 50°
  26. 26.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 130° (d) 160°
  27. 27.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) 105° (c) 15° (d) 75°
  28. 28.Two angles of a triangle are 25° and 100°. What is the exterior angle at the third corner? (a) 155° (b) 55° (c) 125° (d) 80°
  29. 29.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 100° (b) 155° (c) 105° (d) 75°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 10° (c) 50° (d) 100°
  31. 31.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 110° (c) 55° (d) 145°
  32. 32.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 150° (d) 30°
  33. 33.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 60° (c) 150° (d) 30°
  34. 34.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 125° (b) 140° (c) 85° (d) 95°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 60° (d) 70°
  36. 36.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 80° (c) 260° (d) 100°
  37. 37.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 110° (b) 125° (c) 55° (d) 235°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 20° (c) 55° (d) 110°
  39. 39.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 60° (b) 155° (c) 145° (d) 120°
  40. 40.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 30° (d) 75°

Answer key

  1. 110°
  2. 20°
  3. 10°
  4. 10°
  5. 70°
  6. 35°
  7. 55°
  8. 45°
  9. 120°
  10. 50°
  11. 150°
  12. 45°
  13. 80°
  14. 35°
  15. 80°
  16. 70°
  17. 10°
  18. 80°
  19. 85°
  20. 60°
  21. 60°
  22. 95°
  23. 120°
  24. 130°
  25. 150°
  26. 70°
  27. 105°
  28. 125°
  29. 75°
  30. 50°
  31. 110°
  32. 150°
  33. 150°
  34. 95°
  35. 60°
  36. 100°
  37. 55°
  38. 55°
  39. 60°
  40. 30°

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