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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 163 · 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. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 190° (c) 10° (d) 170°
  2. 2.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 210° (b) 105° (c) 30° (d) 150°
  3. 3.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 160° (b) 70° (c) 130° (d) 110°
  4. 4.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 160° (b) 135° (c) 115° (d) 65°
  5. 5.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 120° (d) 85°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 140° (c) 70° (d) 71°
  7. 7.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 50° (d) 130°
  8. 8.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 60° (b) 115° (c) 125° (d) 120°
  9. 9.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 60° (b) 130° (c) 170° (d) 10°
  10. 10.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 250° (b) 140° (c) 70° (d) 110°
  11. 11.Two angles of a triangle are 60° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 240° (d) 121°
  12. 12.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 135° (b) 115° (c) 45° (d) 110°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 50° (d) 100°
  14. 14.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 120° (b) 100° (c) 80° (d) 160°
  15. 15.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 85° (b) 95° (c) 105° (d) 160°
  16. 16.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 130° (b) 80° (c) 150° (d) 100°
  17. 17.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 90° (b) 45° (c) 135° (d) 225°
  18. 18.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 50° (c) 40° (d) 140°
  19. 19.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 90° (c) 270° (d) 110°
  20. 20.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 60° (c) 150° (d) 30°
  21. 21.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 145° (b) 130° (c) 95° (d) 85°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 310° (c) 130° (d) 155°
  23. 23.Two angles of a triangle are 45° and 120°. What is the third angle? (a) 135° (b) 60° (c) 15° (d) 165°
  24. 24.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 30° (b) 210° (c) 150° (d) 60°
  25. 25.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 155° (b) 115° (c) 25° (d) 90°
  26. 26.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 75°
  27. 27.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 255° (b) 75° (c) 105° (d) 150°
  28. 28.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 125° (b) 135° (c) 80° (d) 100°
  29. 29.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 100° (d) 125°
  30. 30.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 136° (c) 135° (d) 315°
  31. 31.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 25° (c) 205° (d) 26°
  32. 32.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 40° (c) 140° (d) 150°
  33. 33.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 325° (c) 145° (d) 55°
  34. 34.Two angles of a triangle are 35° and 100°. What is the third angle? (a) 145° (b) 135° (c) 80° (d) 45°
  35. 35.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 105° (b) 75° (c) 150° (d) 255°
  36. 36.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 135° (b) 140° (c) 85° (d) 95°
  37. 37.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 50° (b) 160° (c) 30° (d) 150°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 56° (c) 55° (d) 125°
  39. 39.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 290° (b) 145° (c) 70° (d) 110°
  40. 40.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 40° (b) 105° (c) 115° (d) 140°

Answer key

  1. 10°
  2. 30°
  3. 70°
  4. 115°
  5. 95°
  6. 70°
  7. 130°
  8. 60°
  9. 10°
  10. 70°
  11. 120°
  12. 45°
  13. 40°
  14. 100°
  15. 85°
  16. 100°
  17. 45°
  18. 140°
  19. 90°
  20. 120°
  21. 95°
  22. 155°
  23. 15°
  24. 150°
  25. 25°
  26. 75°
  27. 105°
  28. 80°
  29. 80°
  30. 135°
  31. 25°
  32. 140°
  33. 145°
  34. 45°
  35. 75°
  36. 95°
  37. 150°
  38. 55°
  39. 110°
  40. 140°

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