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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 788 · 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 35° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 60° (d) 95°
  2. 2.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 150° (b) 95° (c) 125° (d) 85°
  3. 3.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 80° (b) 260° (c) 100° (d) 160°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 30° (d) 75°
  5. 5.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 55° (b) 145° (c) 35° (d) 160°
  6. 6.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 75° (c) 105° (d) 145°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 50° (c) 130° (d) 40°
  8. 8.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 145° (b) 80° (c) 100° (d) 115°
  9. 9.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 155° (c) 60° (d) 145°
  10. 10.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 85° (b) 170° (c) 105° (d) 10°
  11. 11.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 135° (b) 100° (c) 145° (d) 80°
  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.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 120° (c) 60° (d) 240°
  14. 14.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 30° (b) 150° (c) 90° (d) 120°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 70° (d) 55°
  16. 16.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 45° (b) 160° (c) 135° (d) 155°
  17. 17.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 26° (c) 25° (d) 155°
  18. 18.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 86° (d) 265°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 300° (d) 150°
  20. 20.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 160° (c) 105° (d) 85°
  21. 21.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 155° (b) 65° (c) 140° (d) 40°
  22. 22.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 55° (d) 125°
  23. 23.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 45° (b) 105° (c) 120° (d) 135°
  24. 24.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 60° (b) 120° (c) 80° (d) 160°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 20° (b) 80° (c) 200° (d) 100°
  26. 26.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 60° (b) 300° (c) 150° (d) 120°
  27. 27.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 45° (c) 135° (d) 90°
  28. 28.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 80° (b) 115° (c) 145° (d) 100°
  29. 29.Two angles of a triangle are 25° and 90°. What is the third angle? (a) 65° (b) 155° (c) 90° (d) 115°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 45° (c) 35° (d) 70°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 50° (b) 25° (c) 155° (d) 26°
  32. 32.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 40° (d) 140°
  33. 33.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 10° (c) 5° (d) 85°
  34. 34.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 90° (b) 155° (c) 115° (d) 270°
  35. 35.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 150° (d) 100°
  36. 36.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 145° (d) 110°
  37. 37.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 50° (b) 155° (c) 130° (d) 310°
  38. 38.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 105° (d) 115°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 80° (d) 70°
  40. 40.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°

Answer key

  1. 120°
  2. 95°
  3. 80°
  4. 75°
  5. 35°
  6. 75°
  7. 65°
  8. 80°
  9. 60°
  10. 10°
  11. 100°
  12. 80°
  13. 120°
  14. 30°
  15. 55°
  16. 45°
  17. 25°
  18. 85°
  19. 150°
  20. 95°
  21. 140°
  22. 125°
  23. 45°
  24. 60°
  25. 100°
  26. 120°
  27. 90°
  28. 100°
  29. 65°
  30. 35°
  31. 25°
  32. 100°
  33. 10°
  34. 90°
  35. 110°
  36. 110°
  37. 130°
  38. 105°
  39. 80°
  40. 10°

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