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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 89 · 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. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 160° (c) 81° (d) 100°
  2. 2.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 145° (b) 55° (c) 125° (d) 90°
  3. 3.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 125° (b) 95° (c) 140° (d) 55°
  4. 4.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 105° (c) 75° (d) 160°
  5. 5.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 55° (b) 120° (c) 115° (d) 125°
  6. 6.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 30° (c) 105° (d) 15°
  7. 7.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 85° (d) 120°
  8. 8.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 80° (d) 20°
  9. 9.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 120° (b) 60° (c) 160° (d) 140°
  10. 10.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 80° (c) 260° (d) 81°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 130° (c) 50° (d) 40°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 120° (c) 60° (d) 30°
  13. 13.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 100° (d) 70°
  14. 14.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) 46° (d) 90°
  15. 15.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 160° (b) 45° (c) 135° (d) 155°
  16. 16.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 50° (b) 160° (c) 150° (d) 20°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 100° (c) 80° (d) 20°
  18. 18.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 120° (d) 160°
  19. 19.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 160° (b) 320° (c) 140° (d) 40°
  20. 20.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 70° (b) 130° (c) 110° (d) 160°
  21. 21.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 160° (b) 90° (c) 110° (d) 270°
  22. 22.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 85° (b) 95° (c) 150° (d) 115°
  23. 23.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 120° (b) 135° (c) 60° (d) 105°
  24. 24.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 110° (c) 85° (d) 15°
  25. 25.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 125° (b) 35° (c) 305° (d) 55°
  26. 26.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 95° (c) 5° (d) 85°
  27. 27.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 120° (c) 115° (d) 65°
  28. 28.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) 70° (d) 80°
  29. 29.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 110° (b) 125° (c) 235° (d) 55°
  30. 30.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 75° (c) 285° (d) 105°
  31. 31.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 70° (d) 140°
  32. 32.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°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 45° (c) 110° (d) 70°
  34. 34.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 41° (c) 220° (d) 140°
  35. 35.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 55° (b) 125° (c) 135° (d) 100°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 100° (c) 51° (d) 50°
  37. 37.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 40° (d) 70°
  38. 38.Two angles of a triangle are 45° and 75°. What is the exterior angle at the third corner? (a) 60° (b) 135° (c) 105° (d) 120°
  39. 39.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 80° (b) 100° (c) 135° (d) 125°
  40. 40.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 55° (c) 35° (d) 110°

Answer key

  1. 80°
  2. 125°
  3. 125°
  4. 75°
  5. 125°
  6. 30°
  7. 95°
  8. 20°
  9. 120°
  10. 80°
  11. 65°
  12. 60°
  13. 110°
  14. 45°
  15. 45°
  16. 20°
  17. 100°
  18. 80°
  19. 140°
  20. 110°
  21. 90°
  22. 85°
  23. 60°
  24. 15°
  25. 125°
  26. 95°
  27. 115°
  28. 80°
  29. 125°
  30. 105°
  31. 70°
  32. 10°
  33. 35°
  34. 40°
  35. 55°
  36. 50°
  37. 40°
  38. 120°
  39. 80°
  40. 110°

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