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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 17 · 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 45° and 20°. What is the third angle? (a) 160° (b) 65° (c) 115° (d) 135°
  2. 2.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 55° (c) 35° (d) 125°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 50° (c) 130° (d) 40°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 110° (c) 145° (d) 290°
  5. 5.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 155° (b) 90° (c) 115° (d) 65°
  6. 6.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 135° (b) 95° (c) 50° (d) 130°
  7. 7.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 75° (b) 40° (c) 140° (d) 145°
  8. 8.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 125° (b) 145° (c) 160° (d) 55°
  9. 9.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 100° (d) 230°
  10. 10.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 70° (b) 110° (c) 105° (d) 145°
  11. 11.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 65° (b) 245° (c) 130° (d) 115°
  12. 12.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 40° (b) 160° (c) 200° (d) 20°
  13. 13.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°
  14. 14.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 60° (d) 120°
  15. 15.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 80° (d) 40°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 150° (c) 30° (d) 60°
  17. 17.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 30° (c) 60° (d) 150°
  18. 18.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 80° (b) 105° (c) 155° (d) 100°
  19. 19.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 65° (b) 155° (c) 140° (d) 115°
  20. 20.Two angles of a triangle are 40° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 140° (c) 90° (d) 270°
  21. 21.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 100° (b) 120° (c) 160° (d) 80°
  22. 22.Two angles of a triangle are 25° and 60°. What is the third angle? (a) 155° (b) 95° (c) 120° (d) 85°
  23. 23.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 85° (b) 145° (c) 95° (d) 130°
  24. 24.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 140° (d) 40°
  25. 25.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 110° (b) 155° (c) 95° (d) 70°
  26. 26.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 80° (b) 140° (c) 100° (d) 120°
  27. 27.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 140° (d) 100°
  28. 28.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 145° (d) 120°
  29. 29.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 30° (c) 105° (d) 75°
  30. 30.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 125° (b) 55° (c) 35° (d) 305°
  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.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 40° (d) 30°
  33. 33.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 125° (b) 130° (c) 50° (d) 105°
  34. 34.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 35° (c) 55° (d) 145°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 70° (c) 120° (d) 60°
  36. 36.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 120° (b) 155° (c) 60° (d) 145°
  37. 37.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 100° (d) 150°
  38. 38.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 145° (b) 35° (c) 95° (d) 120°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 70° (d) 80°
  40. 40.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 120° (d) 60°

Answer key

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

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