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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 49 · 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 20° and 125°. What is the third angle? (a) 145° (b) 55° (c) 160° (d) 35°
  2. 2.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 40° (c) 80° (d) 130°
  3. 3.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 160° (b) 145° (c) 55° (d) 125°
  4. 4.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 135° (b) 140° (c) 40° (d) 85°
  5. 5.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 15° (c) 75° (d) 105°
  6. 6.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 125° (b) 105° (c) 130° (d) 50°
  7. 7.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 130° (b) 145° (c) 85° (d) 50°
  8. 8.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 15° (b) 100° (c) 95° (d) 165°
  9. 9.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 145° (b) 115° (c) 150° (d) 65°
  10. 10.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 40° (b) 145° (c) 140° (d) 75°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 170° (c) 11° (d) 10°
  12. 12.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 65° (b) 105° (c) 115° (d) 140°
  13. 13.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 70° (d) 120°
  14. 14.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 145° (d) 105°
  15. 15.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 215° (d) 36°
  16. 16.Two angles of a triangle are 40° and 70°. What is the exterior angle at the third corner? (a) 250° (b) 70° (c) 110° (d) 140°
  17. 17.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 115° (b) 130° (c) 65° (d) 245°
  18. 18.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 95° (b) 130° (c) 85° (d) 145°
  19. 19.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 125° (b) 100° (c) 80° (d) 135°
  20. 20.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 50° (c) 65° (d) 115°
  21. 21.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 130° (d) 65°
  22. 22.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 80° (b) 130° (c) 100° (d) 260°
  23. 23.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 220° (b) 110° (c) 140° (d) 40°
  24. 24.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 25° (b) 155° (c) 140° (d) 65°
  25. 25.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 85° (b) 125° (c) 150° (d) 95°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 70° (d) 35°
  27. 27.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 55° (c) 145° (d) 35°
  28. 28.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 120° (b) 60° (c) 30° (d) 300°
  29. 29.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 55° (b) 125° (c) 160° (d) 145°
  30. 30.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 120° (b) 110° (c) 50° (d) 130°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 40° (c) 140° (d) 80°
  32. 32.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 31° (c) 210° (d) 30°
  33. 33.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 20° (c) 200° (d) 21°
  34. 34.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 150° (b) 70° (c) 40° (d) 140°
  35. 35.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 35° (c) 145° (d) 150°
  36. 36.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 140° (b) 100° (c) 120° (d) 40°
  37. 37.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 75°
  38. 38.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 90° (b) 110° (c) 160° (d) 70°
  39. 39.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 205° (c) 25° (d) 26°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 150° (c) 75° (d) 76°

Answer key

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

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