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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 997 · 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 250°. What is each of the other two angles? (a) 110° (b) 125° (c) 56° (d) 55°
  2. 2.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 140° (c) 60° (d) 100°
  3. 3.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 125° (d) 75°
  4. 4.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 110° (b) 100° (c) 150° (d) 80°
  5. 5.Two angles of a triangle are 20° and 60°. What is the third angle? (a) 120° (b) 80° (c) 160° (d) 100°
  6. 6.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 135° (c) 91° (d) 45°
  7. 7.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 145° (d) 35°
  8. 8.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 70° (c) 20° (d) 110°
  9. 9.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 105° (b) 160° (c) 95° (d) 85°
  10. 10.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 125° (c) 100° (d) 135°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 250° (c) 55° (d) 125°
  12. 12.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 140° (b) 135° (c) 95° (d) 85°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 210° (c) 30° (d) 75°
  14. 14.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 135° (b) 110° (c) 115° (d) 70°
  15. 15.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) 50° (d) 100°
  16. 16.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 75° (d) 30°
  17. 17.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 115° (c) 25° (d) 50°
  18. 18.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) 86° (c) 85° (d) 95°
  19. 19.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 50° (d) 100°
  20. 20.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 155° (b) 130° (c) 75° (d) 105°
  21. 21.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 160° (b) 130° (c) 50° (d) 150°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 130° (c) 50° (d) 65°
  23. 23.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 70° (c) 20° (d) 160°
  24. 24.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 270° (b) 140° (c) 130° (d) 90°
  25. 25.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 155° (b) 140° (c) 65° (d) 115°
  26. 26.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 55° (c) 35° (d) 70°
  27. 27.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 170° (b) 10° (c) 80° (d) 110°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 120° (c) 60° (d) 61°
  29. 29.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 100° (b) 155° (c) 75° (d) 105°
  30. 30.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 50° (b) 160° (c) 150° (d) 20°
  31. 31.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 60° (b) 115° (c) 125° (d) 120°
  32. 32.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 25° (b) 155° (c) 70° (d) 135°
  33. 33.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 85° (c) 115° (d) 95°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 50° (d) 70°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 80° (c) 81° (d) 160°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 35° (c) 70° (d) 45°
  37. 37.Two angles of a triangle are 20° and 120°. What is the exterior angle at the third corner? (a) 40° (b) 60° (c) 160° (d) 140°
  38. 38.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 75° (b) 140° (c) 145° (d) 105°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 300° (c) 30° (d) 150°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 200° (c) 20° (d) 100°

Answer key

  1. 55°
  2. 120°
  3. 75°
  4. 80°
  5. 100°
  6. 90°
  7. 145°
  8. 110°
  9. 85°
  10. 135°
  11. 125°
  12. 95°
  13. 105°
  14. 70°
  15. 40°
  16. 30°
  17. 50°
  18. 85°
  19. 100°
  20. 75°
  21. 130°
  22. 65°
  23. 160°
  24. 90°
  25. 115°
  26. 70°
  27. 10°
  28. 60°
  29. 75°
  30. 20°
  31. 60°
  32. 25°
  33. 85°
  34. 70°
  35. 80°
  36. 35°
  37. 140°
  38. 105°
  39. 150°
  40. 100°

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