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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 39 · 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 70° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 135° (c) 110° (d) 115°
  2. 2.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 125° (d) 55°
  3. 3.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 135° (b) 65° (c) 115° (d) 160°
  4. 4.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 160° (d) 70°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 55° (c) 45° (d) 46°
  6. 6.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 150° (b) 255° (c) 105° (d) 75°
  7. 7.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 70° (d) 55°
  8. 8.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 60° (c) 30° (d) 330°
  9. 9.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 160° (b) 40° (c) 320° (d) 140°
  10. 10.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 65° (b) 35° (c) 145° (d) 150°
  11. 11.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 215° (c) 70° (d) 35°
  12. 12.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 55° (b) 235° (c) 56° (d) 125°
  13. 13.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 100° (c) 260° (d) 80°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 80° (c) 100° (d) 10°
  15. 15.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 100° (b) 75° (c) 105° (d) 155°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 50° (d) 140°
  17. 17.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 120° (b) 155° (c) 85° (d) 60°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 60° (c) 120° (d) 61°
  19. 19.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 65° (b) 115° (c) 145° (d) 150°
  20. 20.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 50° (b) 105° (c) 125° (d) 130°
  21. 21.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 110° (b) 150° (c) 140° (d) 70°
  22. 22.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 125° (c) 140° (d) 55°
  23. 23.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 25° (b) 155° (c) 55° (d) 150°
  24. 24.Two angles of a triangle are 55° and 95°. What is the third angle? (a) 30° (b) 125° (c) 85° (d) 150°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 51° (c) 100° (d) 50°
  26. 26.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 61° (c) 60° (d) 30°
  27. 27.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 90° (b) 150° (c) 270° (d) 120°
  28. 28.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 235° (b) 55° (c) 125° (d) 110°
  29. 29.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 100° (d) 70°
  30. 30.Two angles of a triangle are 40° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 65° (c) 115° (d) 140°
  31. 31.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 115° (b) 65° (c) 295° (d) 25°
  32. 32.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 95° (b) 60° (c) 120° (d) 145°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 130° (d) 260°
  34. 34.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 80° (d) 160°
  35. 35.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 140° (b) 110° (c) 70° (d) 150°
  36. 36.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 115° (d) 80°
  37. 37.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 46° (c) 45° (d) 225°
  38. 38.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 160° (b) 100° (c) 260° (d) 80°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 150° (c) 30° (d) 15°
  40. 40.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 150° (b) 60° (c) 30° (d) 210°

Answer key

  1. 115°
  2. 125°
  3. 65°
  4. 70°
  5. 45°
  6. 105°
  7. 70°
  8. 150°
  9. 140°
  10. 35°
  11. 35°
  12. 55°
  13. 100°
  14. 50°
  15. 75°
  16. 70°
  17. 60°
  18. 60°
  19. 115°
  20. 130°
  21. 110°
  22. 125°
  23. 25°
  24. 30°
  25. 50°
  26. 60°
  27. 90°
  28. 125°
  29. 110°
  30. 115°
  31. 115°
  32. 60°
  33. 130°
  34. 80°
  35. 70°
  36. 100°
  37. 45°
  38. 80°
  39. 15°
  40. 150°

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