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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 634 · 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 straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 130° (b) 65° (c) 115° (d) 66°
  2. 2.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 140° (b) 105° (c) 115° (d) 75°
  3. 3.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 95° (b) 40° (c) 125° (d) 140°
  4. 4.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 160° (b) 115° (c) 135° (d) 65°
  5. 5.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 40° (c) 320° (d) 140°
  6. 6.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 100° (b) 115° (c) 145° (d) 65°
  7. 7.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 120° (c) 145° (d) 95°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 155° (b) 50° (c) 25° (d) 26°
  9. 9.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 115° (b) 150° (c) 85° (d) 95°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 210° (c) 75° (d) 105°
  11. 11.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 120° (b) 105° (c) 135° (d) 75°
  12. 12.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 155° (b) 140° (c) 65° (d) 115°
  13. 13.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 135° (c) 95° (d) 85°
  14. 14.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 105° (b) 75° (c) 255° (d) 150°
  15. 15.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 160° (b) 260° (c) 80° (d) 100°
  16. 16.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 140° (b) 105° (c) 115° (d) 40°
  17. 17.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 160° (b) 115° (c) 20° (d) 85°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 150° (c) 30° (d) 60°
  19. 19.Two angles of a triangle are 45° and 65°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 135° (d) 70°
  20. 20.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 105° (b) 35° (c) 145° (d) 110°
  21. 21.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 35° (b) 215° (c) 145° (d) 36°
  22. 22.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 130° (b) 70° (c) 160° (d) 110°
  23. 23.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 140° (b) 155° (c) 65° (d) 25°
  24. 24.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 120° (b) 140° (c) 100° (d) 40°
  25. 25.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°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 60° (c) 30° (d) 120°
  27. 27.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 160° (b) 260° (c) 80° (d) 100°
  28. 28.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 20° (c) 110° (d) 40°
  29. 29.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 125° (d) 130°
  30. 30.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 10° (c) 95° (d) 85°
  31. 31.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 10° (b) 170° (c) 160° (d) 30°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 36° (c) 145° (d) 70°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 260° (c) 80° (d) 130°
  34. 34.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 50° (d) 25°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 90° (d) 45°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 280° (c) 100° (d) 140°
  37. 37.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 50° (b) 100° (c) 230° (d) 130°
  38. 38.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 60° (b) 155° (c) 120° (d) 145°
  39. 39.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 155° (b) 160° (c) 45° (d) 135°
  40. 40.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 45° (d) 135°

Answer key

  1. 65°
  2. 75°
  3. 40°
  4. 65°
  5. 40°
  6. 65°
  7. 95°
  8. 25°
  9. 85°
  10. 105°
  11. 75°
  12. 115°
  13. 85°
  14. 75°
  15. 100°
  16. 40°
  17. 20°
  18. 75°
  19. 110°
  20. 35°
  21. 35°
  22. 110°
  23. 25°
  24. 40°
  25. 25°
  26. 30°
  27. 80°
  28. 40°
  29. 105°
  30. 10°
  31. 10°
  32. 35°
  33. 130°
  34. 50°
  35. 45°
  36. 140°
  37. 130°
  38. 60°
  39. 135°
  40. 135°

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