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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 150 · 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) 125° (b) 100° (c) 155° (d) 80°
  2. 2.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 140° (d) 40°
  3. 3.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 160° (b) 20° (c) 105° (d) 95°
  4. 4.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 230° (c) 130° (d) 50°
  5. 5.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 110° (c) 90° (d) 270°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 65° (d) 130°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 80° (c) 160° (d) 70°
  8. 8.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 110° (d) 145°
  9. 9.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 105° (b) 140° (c) 65° (d) 115°
  10. 10.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 65° (b) 150° (c) 115° (d) 145°
  11. 11.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 65°
  12. 12.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 105° (c) 15° (d) 285°
  13. 13.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 105° (b) 130° (c) 75° (d) 125°
  14. 14.Two angles of a triangle are 25° and 75°. What is the third angle? (a) 80° (b) 100° (c) 105° (d) 155°
  15. 15.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 125° (b) 65° (c) 115° (d) 120°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 11° (c) 20° (d) 10°
  17. 17.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 100° (b) 125° (c) 80° (d) 155°
  18. 18.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 65° (b) 66° (c) 245° (d) 115°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 10° (b) 95° (c) 190° (d) 85°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 50° (b) 155° (c) 25° (d) 26°
  21. 21.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 300° (d) 150°
  22. 22.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 70° (d) 100°
  23. 23.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 115° (b) 25° (c) 155° (d) 90°
  24. 24.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 300° (c) 30° (d) 120°
  25. 25.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 135° (c) 70° (d) 110°
  26. 26.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 86° (c) 95° (d) 265°
  27. 27.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 95° (b) 145° (c) 85° (d) 130°
  28. 28.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) 105° (c) 75° (d) 255°
  29. 29.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 150° (d) 155°
  30. 30.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 30° (b) 120° (c) 150° (d) 90°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 46° (c) 55° (d) 90°
  32. 32.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 160° (b) 100° (c) 200° (d) 20°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 320° (c) 140° (d) 160°
  34. 34.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 140° (c) 280° (d) 100°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 100° (c) 130° (d) 50°
  36. 36.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 70° (b) 125° (c) 165° (d) 15°
  37. 37.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 135° (b) 110° (c) 70° (d) 155°
  38. 38.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 140° (b) 220° (c) 80° (d) 40°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 30° (c) 20° (d) 140°
  40. 40.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 115° (b) 20° (c) 85° (d) 160°

Answer key

  1. 80°
  2. 140°
  3. 20°
  4. 50°
  5. 90°
  6. 65°
  7. 80°
  8. 105°
  9. 65°
  10. 115°
  11. 65°
  12. 105°
  13. 75°
  14. 80°
  15. 65°
  16. 10°
  17. 100°
  18. 65°
  19. 95°
  20. 25°
  21. 60°
  22. 110°
  23. 25°
  24. 120°
  25. 70°
  26. 85°
  27. 85°
  28. 75°
  29. 55°
  30. 150°
  31. 45°
  32. 20°
  33. 160°
  34. 80°
  35. 50°
  36. 15°
  37. 110°
  38. 140°
  39. 20°
  40. 20°

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