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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 507 · 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 70°. What is the third angle? (a) 55° (b) 110° (c) 235° (d) 125°
  2. 2.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 270° (b) 130° (c) 90° (d) 140°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 115° (c) 65° (d) 50°
  4. 4.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 100° (d) 135°
  5. 5.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 225° (b) 135° (c) 45° (d) 90°
  6. 6.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 280° (c) 100° (d) 80°
  7. 7.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 110° (c) 55° (d) 35°
  8. 8.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°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 10° (c) 160° (d) 11°
  10. 10.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 45° (b) 105° (c) 120° (d) 135°
  11. 11.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 60° (c) 30° (d) 120°
  12. 12.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 80° (c) 100° (d) 81°
  13. 13.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 61° (c) 30° (d) 120°
  14. 14.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 15° (c) 110° (d) 85°
  15. 15.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 145° (b) 110° (c) 105° (d) 35°
  16. 16.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 160° (c) 120° (d) 60°
  17. 17.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 145° (b) 130° (c) 50° (d) 85°
  18. 18.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 65° (b) 115° (c) 160° (d) 135°
  19. 19.Two angles of a triangle are 65° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 75° (c) 115° (d) 105°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 65° (c) 130° (d) 50°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 160° (c) 320° (d) 20°
  22. 22.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 40° (b) 75° (c) 140° (d) 145°
  23. 23.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 71° (c) 70° (d) 110°
  24. 24.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 130° (d) 120°
  25. 25.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 35° (b) 120° (c) 95° (d) 145°
  26. 26.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 120° (b) 150° (c) 90° (d) 270°
  27. 27.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 105° (b) 255° (c) 150° (d) 75°
  28. 28.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 60° (b) 120° (c) 145° (d) 155°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 155° (c) 130° (d) 310°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 45° (c) 46° (d) 90°
  31. 31.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 60° (d) 120°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 70° (d) 50°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 220° (c) 110° (d) 40°
  34. 34.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 160° (b) 155° (c) 45° (d) 20°
  35. 35.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 145° (d) 35°
  36. 36.Two angles of a triangle are 25° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 125° (c) 55° (d) 155°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 45° (c) 90° (d) 46°
  38. 38.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 135° (b) 160° (c) 115° (d) 65°
  39. 39.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) 330° (c) 150° (d) 60°
  40. 40.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 70° (b) 135° (c) 45° (d) 155°

Answer key

  1. 55°
  2. 90°
  3. 115°
  4. 125°
  5. 45°
  6. 100°
  7. 110°
  8. 50°
  9. 10°
  10. 45°
  11. 120°
  12. 80°
  13. 60°
  14. 15°
  15. 35°
  16. 120°
  17. 130°
  18. 115°
  19. 105°
  20. 65°
  21. 160°
  22. 40°
  23. 70°
  24. 110°
  25. 35°
  26. 90°
  27. 75°
  28. 120°
  29. 155°
  30. 45°
  31. 120°
  32. 70°
  33. 110°
  34. 20°
  35. 145°
  36. 125°
  37. 45°
  38. 65°
  39. 150°
  40. 45°

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