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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 207 · 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. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 71° (c) 110° (d) 250°
  2. 2.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 160° (b) 120° (c) 60° (d) 140°
  3. 3.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 160° (c) 200° (d) 20°
  4. 4.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 160° (c) 65° (d) 135°
  5. 5.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 125° (d) 90°
  6. 6.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 235° (c) 56° (d) 55°
  7. 7.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 60° (c) 150° (d) 330°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 25° (c) 35° (d) 130°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 320° (c) 140° (d) 160°
  10. 10.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 95° (c) 265° (d) 85°
  11. 11.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 61° (c) 120° (d) 60°
  12. 12.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 90° (b) 145° (c) 55° (d) 125°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 120° (c) 60° (d) 240°
  14. 14.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 135° (b) 100° (c) 55° (d) 125°
  15. 15.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°
  16. 16.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 45° (b) 125° (c) 135° (d) 100°
  17. 17.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 115° (b) 105° (c) 40° (d) 140°
  18. 18.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 15° (c) 105° (d) 30°
  19. 19.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 140° (b) 80° (c) 100° (d) 120°
  20. 20.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 25° (b) 150° (c) 155° (d) 55°
  21. 21.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 170° (b) 10° (c) 105° (d) 85°
  22. 22.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 50° (c) 115° (d) 65°
  23. 23.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 125° (b) 120° (c) 115° (d) 55°
  24. 24.Two angles of a triangle are 45° and 70°. What is the exterior angle at the third corner? (a) 65° (b) 135° (c) 115° (d) 110°
  25. 25.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 20° (c) 70° (d) 110°
  26. 26.Two angles of a triangle are 45° and 75°. What is the exterior angle at the third corner? (a) 120° (b) 135° (c) 105° (d) 60°
  27. 27.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 155° (b) 85° (c) 120° (d) 95°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 140° (c) 100° (d) 280°
  29. 29.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 285° (c) 15° (d) 105°
  30. 30.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 75° (b) 145° (c) 140° (d) 105°
  31. 31.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 75° (c) 105° (d) 150°
  32. 32.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 260° (d) 81°
  33. 33.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 105° (c) 160° (d) 75°
  34. 34.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 25° (b) 155° (c) 70° (d) 135°
  35. 35.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 125° (b) 85° (c) 150° (d) 30°
  36. 36.Two angles of a triangle are 25° and 25°. What is the exterior angle at the third corner? (a) 130° (b) 155° (c) 310° (d) 50°
  37. 37.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 80° (d) 100°
  38. 38.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 55° (b) 325° (c) 35° (d) 145°
  39. 39.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 25° (c) 155° (d) 130°
  40. 40.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 135° (c) 100° (d) 125°

Answer key

  1. 70°
  2. 120°
  3. 20°
  4. 65°
  5. 145°
  6. 55°
  7. 150°
  8. 25°
  9. 160°
  10. 85°
  11. 60°
  12. 55°
  13. 120°
  14. 55°
  15. 20°
  16. 45°
  17. 40°
  18. 30°
  19. 80°
  20. 25°
  21. 10°
  22. 50°
  23. 125°
  24. 115°
  25. 40°
  26. 120°
  27. 85°
  28. 140°
  29. 105°
  30. 105°
  31. 75°
  32. 80°
  33. 105°
  34. 25°
  35. 150°
  36. 50°
  37. 100°
  38. 145°
  39. 130°
  40. 100°

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