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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 480 · 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 70° and 80°. What is the third angle? (a) 150° (b) 100° (c) 110° (d) 30°
  2. 2.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 135° (b) 120° (c) 75° (d) 105°
  3. 3.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 50° (d) 100°
  4. 4.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 125° (b) 140° (c) 85° (d) 95°
  5. 5.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 95° (c) 85° (d) 5°
  6. 6.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 150° (b) 80° (c) 50° (d) 130°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 50° (c) 115° (d) 65°
  8. 8.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 135° (b) 110° (c) 115° (d) 70°
  9. 9.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 110° (c) 70° (d) 40°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 70° (d) 30°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 20° (c) 100° (d) 80°
  12. 12.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 60° (c) 330° (d) 30°
  13. 13.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 120° (d) 160°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 70° (c) 20° (d) 55°
  15. 15.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 40° (d) 80°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 20° (c) 40° (d) 30°
  17. 17.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 155° (b) 145° (c) 60° (d) 120°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 75° (b) 150° (c) 76° (d) 105°
  19. 19.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 125° (b) 95° (c) 150° (d) 85°
  20. 20.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 150° (d) 140°
  21. 21.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 70° (c) 35° (d) 125°
  22. 22.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 315° (c) 45° (d) 135°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 170° (c) 10° (d) 11°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 100° (b) 50° (c) 130° (d) 51°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 20° (c) 11° (d) 160°
  26. 26.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 100° (c) 20° (d) 80°
  27. 27.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 145° (b) 80° (c) 100° (d) 135°
  28. 28.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 145° (b) 125° (c) 160° (d) 55°
  29. 29.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 80° (d) 100°
  30. 30.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 95° (b) 140° (c) 85° (d) 125°
  31. 31.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 85° (c) 105° (d) 95°
  32. 32.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 135° (d) 110°
  33. 33.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 150° (b) 95° (c) 115° (d) 30°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 120° (b) 60° (c) 240° (d) 121°
  35. 35.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 40° (c) 130° (d) 50°
  36. 36.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 160° (c) 75° (d) 125°
  37. 37.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 115° (b) 160° (c) 135° (d) 65°
  38. 38.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 150° (b) 105° (c) 75° (d) 255°
  39. 39.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 50° (b) 130° (c) 125° (d) 105°
  40. 40.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 85° (c) 95° (d) 86°

Answer key

  1. 30°
  2. 75°
  3. 100°
  4. 85°
  5. 10°
  6. 50°
  7. 115°
  8. 70°
  9. 40°
  10. 60°
  11. 100°
  12. 150°
  13. 80°
  14. 55°
  15. 80°
  16. 20°
  17. 60°
  18. 75°
  19. 85°
  20. 70°
  21. 70°
  22. 135°
  23. 10°
  24. 50°
  25. 10°
  26. 20°
  27. 80°
  28. 125°
  29. 100°
  30. 95°
  31. 95°
  32. 115°
  33. 30°
  34. 120°
  35. 130°
  36. 75°
  37. 115°
  38. 75°
  39. 50°
  40. 85°

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