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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 661 · 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 60° and 55°. What is the exterior angle at the third corner? (a) 65° (b) 120° (c) 125° (d) 115°
  2. 2.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 105° (b) 115° (c) 140° (d) 75°
  3. 3.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 115° (b) 40° (c) 140° (d) 105°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 290° (c) 145° (d) 110°
  5. 5.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 115° (b) 60° (c) 120° (d) 125°
  6. 6.Two angles of a triangle are 50° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 140° (c) 130° (d) 40°
  7. 7.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 105° (c) 30° (d) 75°
  8. 8.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 145° (b) 150° (c) 115° (d) 65°
  9. 9.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 90° (b) 110° (c) 160° (d) 20°
  10. 10.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 70° (b) 135° (c) 110° (d) 115°
  11. 11.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 55° (b) 235° (c) 110° (d) 125°
  12. 12.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 40° (c) 110° (d) 20°
  13. 13.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 150° (b) 90° (c) 60° (d) 120°
  14. 14.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 150° (b) 100° (c) 110° (d) 80°
  15. 15.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 140° (c) 40° (d) 320°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 125° (c) 110° (d) 55°
  17. 17.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 150° (b) 115° (c) 95° (d) 85°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 160° (c) 80° (d) 81°
  19. 19.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 70° (d) 55°
  20. 20.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 160° (b) 125° (c) 105° (d) 75°
  21. 21.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 110° (d) 35°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 150° (c) 300° (d) 120°
  23. 23.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 65° (b) 135° (c) 110° (d) 115°
  24. 24.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 115° (d) 35°
  25. 25.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 105° (d) 75°
  26. 26.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 105° (b) 255° (c) 150° (d) 75°
  27. 27.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 40° (b) 220° (c) 110° (d) 140°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 70° (d) 60°
  29. 29.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 55° (b) 170° (c) 10° (d) 135°
  30. 30.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 80° (b) 165° (c) 115° (d) 15°
  31. 31.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 155° (b) 120° (c) 85° (d) 60°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 100° (c) 50° (d) 80°
  33. 33.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 45° (b) 145° (c) 10° (d) 170°
  34. 34.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 50° (c) 130° (d) 51°
  35. 35.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 20° (b) 145° (c) 160° (d) 55°
  36. 36.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 55° (c) 56° (d) 125°
  37. 37.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 110° (b) 290° (c) 70° (d) 20°
  38. 38.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) 70° (d) 110°
  39. 39.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 105° (b) 120° (c) 135° (d) 60°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 15° (c) 30° (d) 16°

Answer key

  1. 115°
  2. 105°
  3. 40°
  4. 145°
  5. 60°
  6. 140°
  7. 30°
  8. 65°
  9. 20°
  10. 70°
  11. 125°
  12. 40°
  13. 120°
  14. 80°
  15. 140°
  16. 55°
  17. 85°
  18. 80°
  19. 70°
  20. 105°
  21. 110°
  22. 150°
  23. 65°
  24. 145°
  25. 105°
  26. 75°
  27. 40°
  28. 60°
  29. 10°
  30. 15°
  31. 60°
  32. 50°
  33. 10°
  34. 50°
  35. 20°
  36. 55°
  37. 110°
  38. 35°
  39. 60°
  40. 15°

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