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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 251 · 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 55° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 125° (c) 100° (d) 80°
  2. 2.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 60° (b) 120° (c) 61° (d) 240°
  3. 3.Two angles of a triangle are 20° and 115°. What is the third angle? (a) 135° (b) 160° (c) 45° (d) 65°
  4. 4.Two angles of a triangle are 70° and 45°. What is the third angle? (a) 65° (b) 110° (c) 115° (d) 135°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 36° (b) 145° (c) 35° (d) 70°
  6. 6.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 335° (c) 25° (d) 65°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 310° (c) 130° (d) 25°
  8. 8.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 110° (b) 100° (c) 150° (d) 70°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 100° (c) 50° (d) 80°
  10. 10.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 155° (b) 120° (c) 60° (d) 85°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 100° (c) 20° (d) 200°
  12. 12.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 130° (c) 40° (d) 310°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 70° (c) 55° (d) 110°
  14. 14.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 125° (b) 235° (c) 55° (d) 110°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 40° (c) 140° (d) 100°
  16. 16.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 260° (b) 100° (c) 130° (d) 80°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 80° (d) 70°
  18. 18.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 125° (b) 100° (c) 135° (d) 45°
  19. 19.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 105° (b) 75° (c) 255° (d) 150°
  20. 20.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 100° (c) 80° (d) 20°
  21. 21.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 120° (b) 60° (c) 140° (d) 100°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 130° (c) 35° (d) 50°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 130° (b) 66° (c) 65° (d) 115°
  24. 24.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 110° (b) 70° (c) 105° (d) 145°
  25. 25.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 160° (b) 85° (c) 95° (d) 105°
  26. 26.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 155° (b) 125° (c) 55° (d) 80°
  27. 27.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 160° (b) 60° (c) 80° (d) 120°
  28. 28.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 65° (b) 295° (c) 25° (d) 115°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 260° (d) 130°
  30. 30.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 110° (b) 160° (c) 90° (d) 70°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 230° (c) 115° (d) 50°
  32. 32.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 70° (c) 55° (d) 35°
  33. 33.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 155° (b) 160° (c) 135° (d) 45°
  34. 34.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 70° (b) 160° (c) 130° (d) 50°
  35. 35.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 25° (b) 155° (c) 105° (d) 100°
  36. 36.Two angles of a triangle are 35° and 100°. What is the third angle? (a) 135° (b) 80° (c) 45° (d) 145°
  37. 37.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 65° (c) 130° (d) 25°
  38. 38.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 160° (d) 135°
  39. 39.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 75° (c) 145° (d) 105°
  40. 40.Two angles of a triangle are 45° and 80°. What is the third angle? (a) 100° (b) 135° (c) 55° (d) 125°

Answer key

  1. 80°
  2. 60°
  3. 45°
  4. 65°
  5. 35°
  6. 155°
  7. 155°
  8. 70°
  9. 50°
  10. 60°
  11. 100°
  12. 130°
  13. 55°
  14. 55°
  15. 140°
  16. 80°
  17. 80°
  18. 45°
  19. 75°
  20. 20°
  21. 60°
  22. 25°
  23. 65°
  24. 70°
  25. 85°
  26. 55°
  27. 60°
  28. 115°
  29. 130°
  30. 70°
  31. 115°
  32. 70°
  33. 45°
  34. 50°
  35. 25°
  36. 45°
  37. 130°
  38. 65°
  39. 105°
  40. 55°

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