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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 156 · 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 50° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 130° (c) 75° (d) 105°
  2. 2.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 100° (b) 15° (c) 95° (d) 165°
  3. 3.Two angles of a triangle are 50° and 40°. What is the third angle? (a) 130° (b) 90° (c) 140° (d) 270°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 86° (c) 85° (d) 95°
  5. 5.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 160° (b) 140° (c) 120° (d) 60°
  6. 6.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 220° (c) 140° (d) 40°
  7. 7.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 75° (b) 120° (c) 105° (d) 135°
  8. 8.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 35° (c) 55° (d) 125°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 75° (b) 105° (c) 150° (d) 76°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 60° (c) 120° (d) 30°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 11° (c) 10° (d) 160°
  12. 12.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 26° (d) 205°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 90° (c) 46° (d) 45°
  14. 14.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°
  15. 15.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 155° (b) 140° (c) 115° (d) 65°
  16. 16.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 40° (b) 140° (c) 85° (d) 135°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 60° (c) 30° (d) 150°
  18. 18.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 35° (d) 100°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 36° (b) 145° (c) 35° (d) 70°
  20. 20.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 150° (b) 55° (c) 30° (d) 155°
  21. 21.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 40° (b) 70° (c) 150° (d) 140°
  22. 22.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 155° (d) 25°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 66° (c) 115° (d) 130°
  24. 24.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 130° (b) 60° (c) 120° (d) 110°
  25. 25.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 40°
  26. 26.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 150° (b) 105° (c) 255° (d) 75°
  27. 27.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 230° (c) 130° (d) 50°
  28. 28.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 55° (c) 145° (d) 35°
  29. 29.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 75° (b) 130° (c) 155° (d) 25°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 100° (d) 50°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 130° (d) 65°
  32. 32.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 110° (d) 145°
  33. 33.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 65° (c) 25° (d) 115°
  34. 34.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 135° (c) 45° (d) 91°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 120° (c) 121° (d) 60°
  36. 36.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 105° (b) 135° (c) 120° (d) 60°
  37. 37.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 105° (c) 85° (d) 160°
  38. 38.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 55° (b) 160° (c) 75° (d) 125°
  39. 39.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 135° (c) 160° (d) 65°
  40. 40.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 70° (b) 160° (c) 130° (d) 110°

Answer key

  1. 75°
  2. 15°
  3. 90°
  4. 85°
  5. 120°
  6. 40°
  7. 75°
  8. 70°
  9. 75°
  10. 30°
  11. 10°
  12. 25°
  13. 45°
  14. 110°
  15. 115°
  16. 40°
  17. 75°
  18. 145°
  19. 35°
  20. 150°
  21. 40°
  22. 130°
  23. 65°
  24. 120°
  25. 40°
  26. 75°
  27. 50°
  28. 145°
  29. 25°
  30. 40°
  31. 65°
  32. 110°
  33. 115°
  34. 90°
  35. 120°
  36. 60°
  37. 95°
  38. 55°
  39. 65°
  40. 110°

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