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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 234 · 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 105°. What is the third angle? (a) 75° (b) 140° (c) 40° (d) 145°
  2. 2.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 25° (c) 115° (d) 65°
  3. 3.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 110° (d) 40°
  4. 4.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 50° (c) 130° (d) 40°
  5. 5.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 70° (d) 140°
  6. 6.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 105° (c) 160° (d) 75°
  7. 7.Two angles of a triangle are 55° and 105°. What is the third angle? (a) 20° (b) 75° (c) 125° (d) 160°
  8. 8.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 160° (b) 60° (c) 120° (d) 80°
  9. 9.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 135° (b) 95° (c) 50° (d) 130°
  10. 10.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 125° (b) 55° (c) 235° (d) 110°
  11. 11.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°
  12. 12.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 70° (b) 160° (c) 130° (d) 110°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 40°
  14. 14.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 125° (d) 70°
  15. 15.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 90° (b) 55° (c) 145° (d) 125°
  16. 16.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 76° (b) 75° (c) 255° (d) 105°
  17. 17.Two angles of a triangle are 25° and 90°. What is the third angle? (a) 115° (b) 155° (c) 90° (d) 65°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 145° (c) 36° (d) 35°
  19. 19.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 120° (d) 60°
  20. 20.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 160° (b) 20° (c) 60° (d) 140°
  21. 21.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 100° (d) 10°
  22. 22.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 160° (b) 60° (c) 120° (d) 140°
  23. 23.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 100° (d) 80°
  24. 24.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 105° (b) 15° (c) 90° (d) 165°
  25. 25.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 40° (c) 50° (d) 80°
  26. 26.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 110° (b) 20° (c) 290° (d) 70°
  27. 27.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 95° (b) 70° (c) 110° (d) 155°
  28. 28.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) 40° (d) 130°
  29. 29.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 155° (b) 20° (c) 160° (d) 45°
  30. 30.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 20° (b) 200° (c) 160° (d) 100°
  31. 31.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 70° (b) 250° (c) 110° (d) 140°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 30° (c) 120° (d) 40°
  33. 33.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 85° (b) 10° (c) 170° (d) 105°
  34. 34.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 36° (b) 145° (c) 215° (d) 35°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 20° (c) 70° (d) 110°
  36. 36.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 90° (d) 125°
  37. 37.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 105° (c) 155° (d) 75°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 50° (b) 25° (c) 155° (d) 26°
  39. 39.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°
  40. 40.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 130° (c) 65° (d) 25°

Answer key

  1. 40°
  2. 115°
  3. 40°
  4. 130°
  5. 70°
  6. 75°
  7. 20°
  8. 120°
  9. 130°
  10. 55°
  11. 20°
  12. 110°
  13. 40°
  14. 70°
  15. 55°
  16. 75°
  17. 65°
  18. 35°
  19. 120°
  20. 20°
  21. 20°
  22. 60°
  23. 100°
  24. 15°
  25. 80°
  26. 110°
  27. 70°
  28. 65°
  29. 20°
  30. 20°
  31. 110°
  32. 30°
  33. 10°
  34. 35°
  35. 55°
  36. 145°
  37. 105°
  38. 25°
  39. 15°
  40. 130°

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