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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 444 · 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 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 140° (d) 100°
  2. 2.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 140° (b) 110° (c) 220° (d) 40°
  3. 3.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 30° (c) 150° (d) 60°
  4. 4.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 230° (c) 50° (d) 130°
  5. 5.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 140° (b) 160° (c) 40° (d) 60°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 80° (c) 50° (d) 10°
  7. 7.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 65° (d) 130°
  8. 8.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 65° (b) 295° (c) 25° (d) 115°
  9. 9.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 50° (b) 110° (c) 120° (d) 130°
  10. 10.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 110° (b) 100° (c) 70° (d) 150°
  11. 11.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 250° (c) 71° (d) 70°
  12. 12.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 105° (b) 100° (c) 25° (d) 155°
  13. 13.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 125° (b) 130° (c) 105° (d) 55°
  14. 14.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 5° (c) 10° (d) 95°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 150° (d) 75°
  16. 16.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 55° (c) 35° (d) 125°
  17. 17.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 125° (d) 70°
  18. 18.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 110° (c) 40° (d) 70°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 140° (d) 50°
  20. 20.Two angles of a triangle are 50° and 40°. What is the third angle? (a) 270° (b) 140° (c) 130° (d) 90°
  21. 21.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 165° (b) 120° (c) 15° (d) 75°
  22. 22.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 10° (c) 280° (d) 100°
  23. 23.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 250° (b) 70° (c) 110° (d) 125°
  24. 24.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 30° (d) 75°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 165° (c) 30° (d) 15°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 100° (d) 40°
  27. 27.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 35° (d) 145°
  28. 28.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 65° (b) 110° (c) 135° (d) 115°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 140° (c) 70° (d) 110°
  30. 30.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 70° (c) 110° (d) 290°
  31. 31.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) 40° (d) 50°
  32. 32.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 80° (d) 20°
  33. 33.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 155° (b) 125° (c) 55° (d) 80°
  34. 34.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 135° (c) 91° (d) 90°
  35. 35.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°
  36. 36.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 75° (b) 120° (c) 135° (d) 105°
  37. 37.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 90° (b) 160° (c) 270° (d) 110°
  38. 38.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 130° (c) 80° (d) 50°
  39. 39.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 110° (b) 30° (c) 100° (d) 150°
  40. 40.Two angles of a triangle are 55° and 50°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 125° (d) 130°

Answer key

  1. 120°
  2. 40°
  3. 150°
  4. 130°
  5. 40°
  6. 50°
  7. 130°
  8. 115°
  9. 50°
  10. 70°
  11. 70°
  12. 25°
  13. 55°
  14. 10°
  15. 75°
  16. 125°
  17. 70°
  18. 40°
  19. 70°
  20. 90°
  21. 15°
  22. 100°
  23. 70°
  24. 30°
  25. 15°
  26. 40°
  27. 145°
  28. 115°
  29. 70°
  30. 70°
  31. 65°
  32. 20°
  33. 55°
  34. 90°
  35. 60°
  36. 75°
  37. 90°
  38. 80°
  39. 30°
  40. 105°

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