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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 452 · 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 50° and 55°. What is the exterior angle at the third corner? (a) 75° (b) 125° (c) 105° (d) 130°
  2. 2.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 140° (d) 250°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 25° (c) 30° (d) 15°
  4. 4.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 40° (d) 130°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 70° (b) 140° (c) 110° (d) 71°
  6. 6.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 80° (d) 140°
  7. 7.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 155° (d) 130°
  8. 8.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 50° (d) 100°
  9. 9.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) 150° (c) 330° (d) 60°
  10. 10.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) 305° (c) 55° (d) 35°
  11. 11.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 270° (c) 90° (d) 120°
  12. 12.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 105° (b) 145° (c) 35° (d) 110°
  13. 13.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 10° (c) 85° (d) 5°
  14. 14.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 90° (b) 270° (c) 120° (d) 150°
  15. 15.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°
  16. 16.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 70° (b) 120° (c) 130° (d) 110°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 100° (c) 10° (d) 80°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 45° (c) 90° (d) 55°
  19. 19.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 155° (b) 95° (c) 85° (d) 110°
  20. 20.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) 105° (d) 15°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 20° (c) 11° (d) 170°
  22. 22.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 135° (b) 45° (c) 155° (d) 160°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 20° (c) 30° (d) 40°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 120° (c) 60° (d) 59°
  25. 25.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 95° (b) 135° (c) 130° (d) 85°
  26. 26.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 65° (b) 90° (c) 155° (d) 115°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 210° (b) 105° (c) 75° (d) 30°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 25° (b) 155° (c) 26° (d) 50°
  29. 29.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 115° (b) 55° (c) 125° (d) 120°
  30. 30.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 80° (b) 130° (c) 150° (d) 100°
  31. 31.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 125° (c) 145° (d) 35°
  32. 32.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 135° (c) 65° (d) 160°
  33. 33.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 140° (c) 41° (d) 220°
  34. 34.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 80° (b) 20° (c) 120° (d) 160°
  35. 35.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 200° (d) 21°
  36. 36.Two angles of a triangle are 60° and 110°. What is the third angle? (a) 10° (b) 120° (c) 170° (d) 70°
  37. 37.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 125° (d) 160°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 75° (d) 60°
  39. 39.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 120° (d) 30°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 50° (c) 130° (d) 40°

Answer key

  1. 105°
  2. 110°
  3. 15°
  4. 80°
  5. 70°
  6. 100°
  7. 75°
  8. 100°
  9. 150°
  10. 125°
  11. 90°
  12. 35°
  13. 10°
  14. 90°
  15. 30°
  16. 110°
  17. 50°
  18. 45°
  19. 85°
  20. 105°
  21. 10°
  22. 135°
  23. 20°
  24. 60°
  25. 95°
  26. 115°
  27. 105°
  28. 25°
  29. 125°
  30. 100°
  31. 145°
  32. 65°
  33. 40°
  34. 20°
  35. 20°
  36. 10°
  37. 75°
  38. 75°
  39. 120°
  40. 65°

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