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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 271 · 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.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 125° (c) 55° (d) 35°
  2. 2.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 55° (c) 100° (d) 125°
  3. 3.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 95° (c) 85° (d) 105°
  4. 4.Two angles of a triangle are 40° and 80°. What is the exterior angle at the third corner? (a) 120° (b) 140° (c) 60° (d) 100°
  5. 5.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 120° (d) 30°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 20° (c) 160° (d) 320°
  7. 7.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 90° (b) 155° (c) 270° (d) 115°
  8. 8.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 80° (b) 155° (c) 25° (d) 125°
  9. 9.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 140° (b) 125° (c) 95° (d) 85°
  10. 10.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 110° (b) 250° (c) 140° (d) 70°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 70° (c) 55° (d) 250°
  12. 12.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 80° (c) 130° (d) 100°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 140° (d) 40°
  14. 14.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 80° (b) 140° (c) 100° (d) 280°
  15. 15.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 145° (c) 65° (d) 30°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 85° (c) 10° (d) 95°
  17. 17.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 56° (c) 125° (d) 55°
  18. 18.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 35° (b) 140° (c) 75° (d) 145°
  19. 19.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 10° (d) 5°
  20. 20.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 110° (c) 70° (d) 20°
  21. 21.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 100° (d) 155°
  22. 22.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 60° (c) 120° (d) 100°
  23. 23.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 30° (c) 150° (d) 31°
  24. 24.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 75° (b) 105° (c) 100° (d) 155°
  25. 25.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 110° (b) 105° (c) 75° (d) 145°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 50° (d) 65°
  27. 27.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 140° (b) 110° (c) 150° (d) 70°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 35° (d) 25°
  29. 29.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 40° (c) 140° (d) 100°
  30. 30.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 130° (b) 80° (c) 150° (d) 100°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 45° (c) 35° (d) 110°
  32. 32.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 60° (c) 330° (d) 150°
  33. 33.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 60° (c) 120° (d) 300°
  34. 34.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 10° (c) 100° (d) 20°
  35. 35.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 115° (c) 50° (d) 65°
  36. 36.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) 65° (d) 66°
  37. 37.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 310° (b) 50° (c) 155° (d) 130°
  38. 38.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 140° (b) 160° (c) 60° (d) 20°
  39. 39.Two angles of a triangle are 25° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 155° (d) 70°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 20° (c) 200° (d) 100°

Answer key

  1. 70°
  2. 125°
  3. 95°
  4. 120°
  5. 120°
  6. 160°
  7. 90°
  8. 25°
  9. 85°
  10. 70°
  11. 125°
  12. 80°
  13. 70°
  14. 100°
  15. 150°
  16. 95°
  17. 55°
  18. 145°
  19. 10°
  20. 110°
  21. 105°
  22. 120°
  23. 30°
  24. 75°
  25. 75°
  26. 65°
  27. 110°
  28. 25°
  29. 100°
  30. 100°
  31. 35°
  32. 150°
  33. 60°
  34. 20°
  35. 50°
  36. 65°
  37. 130°
  38. 20°
  39. 70°
  40. 100°

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