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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 25 · 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 65° and 65°. What is the exterior angle at the third corner? (a) 230° (b) 130° (c) 115° (d) 50°
  2. 2.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 65° (c) 155° (d) 335°
  3. 3.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 95° (b) 155° (c) 110° (d) 70°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 170° (c) 86° (d) 95°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 55° (d) 70°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 110° (c) 145° (d) 35°
  7. 7.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 120° (b) 70° (c) 130° (d) 110°
  8. 8.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 120° (c) 105° (d) 60°
  9. 9.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 55° (b) 160° (c) 145° (d) 125°
  10. 10.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 20° (c) 290° (d) 110°
  11. 11.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°
  12. 12.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 145° (b) 110° (c) 290° (d) 70°
  13. 13.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 15° (b) 165° (c) 120° (d) 75°
  14. 14.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 26° (b) 205° (c) 155° (d) 25°
  15. 15.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) 140° (c) 40° (d) 220°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 11° (c) 10° (d) 20°
  17. 17.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 105° (b) 125° (c) 130° (d) 75°
  18. 18.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 155° (b) 40° (c) 15° (d) 165°
  19. 19.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 50° (b) 125° (c) 130° (d) 105°
  20. 20.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) 330° (c) 60° (d) 150°
  21. 21.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) 100° (c) 10° (d) 280°
  22. 22.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 75° (b) 105° (c) 100° (d) 155°
  23. 23.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 80° (d) 120°
  24. 24.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 95° (b) 45° (c) 135° (d) 130°
  25. 25.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 130° (b) 51° (c) 50° (d) 230°
  26. 26.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 31° (b) 210° (c) 30° (d) 150°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 80° (c) 160° (d) 20°
  28. 28.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 155° (b) 120° (c) 85° (d) 60°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 45° (c) 90° (d) 46°
  30. 30.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 35° (c) 36° (d) 145°
  31. 31.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 115° (c) 66° (d) 65°
  32. 32.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 145° (c) 130° (d) 35°
  33. 33.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 60° (b) 20° (c) 160° (d) 140°
  34. 34.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) 71° (c) 70° (d) 250°
  35. 35.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 110° (d) 155°
  36. 36.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 145° (d) 290°
  37. 37.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 81° (c) 80° (d) 260°
  38. 38.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 150° (b) 140° (c) 70° (d) 110°
  39. 39.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 295° (c) 115° (d) 65°
  40. 40.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 70° (c) 40° (d) 20°

Answer key

  1. 130°
  2. 155°
  3. 70°
  4. 85°
  5. 55°
  6. 145°
  7. 70°
  8. 120°
  9. 55°
  10. 110°
  11. 65°
  12. 110°
  13. 15°
  14. 25°
  15. 40°
  16. 10°
  17. 75°
  18. 15°
  19. 130°
  20. 150°
  21. 100°
  22. 75°
  23. 100°
  24. 45°
  25. 50°
  26. 30°
  27. 80°
  28. 120°
  29. 45°
  30. 35°
  31. 65°
  32. 145°
  33. 20°
  34. 70°
  35. 95°
  36. 70°
  37. 80°
  38. 70°
  39. 115°
  40. 40°

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