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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 106 · 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 30°. What is the angle next to it on the same straight line? (a) 30° (b) 150° (c) 60° (d) 330°
  2. 2.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 40° (d) 130°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 110° (c) 20° (d) 55°
  4. 4.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 50° (b) 130° (c) 155° (d) 75°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 25° (d) 35°
  6. 6.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 30° (d) 61°
  7. 7.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 65° (b) 66° (c) 115° (d) 245°
  8. 8.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 90° (c) 45° (d) 135°
  9. 9.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 220° (b) 40° (c) 140° (d) 80°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 70° (c) 45° (d) 35°
  11. 11.Two angles of a triangle are 55° and 85°. What is the exterior angle at the third corner? (a) 140° (b) 125° (c) 40° (d) 95°
  12. 12.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 120° (c) 60° (d) 300°
  13. 13.Two angles of a triangle are 55° and 50°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 125° (d) 130°
  14. 14.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 75° (b) 255° (c) 76° (d) 105°
  15. 15.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 255° (d) 150°
  16. 16.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 155° (b) 105° (c) 100° (d) 75°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 40° (c) 60° (d) 30°
  18. 18.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 120° (b) 115° (c) 65° (d) 125°
  19. 19.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 95° (b) 125° (c) 40° (d) 140°
  20. 20.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 45° (c) 315° (d) 135°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 100° (b) 130° (c) 51° (d) 50°
  22. 22.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 55° (c) 125° (d) 305°
  23. 23.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 55° (c) 70° (d) 35°
  24. 24.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 90° (b) 155° (c) 270° (d) 115°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 40° (c) 50° (d) 130°
  26. 26.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 115° (b) 125° (c) 120° (d) 65°
  27. 27.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 100° (c) 140° (d) 40°
  28. 28.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 85° (b) 115° (c) 20° (d) 160°
  29. 29.Two angles of a triangle are 25° and 90°. What is the third angle? (a) 90° (b) 115° (c) 65° (d) 155°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 140° (c) 30° (d) 20°
  31. 31.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 50° (b) 310° (c) 130° (d) 155°
  32. 32.Two angles of a triangle are 40° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 270° (c) 90° (d) 140°
  33. 33.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 80° (c) 20° (d) 100°
  34. 34.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 125° (b) 235° (c) 55° (d) 110°
  35. 35.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 270° (b) 150° (c) 120° (d) 90°
  36. 36.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 150° (b) 160° (c) 30° (d) 50°
  37. 37.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 105° (b) 10° (c) 170° (d) 85°
  38. 38.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 115° (b) 105° (c) 75° (d) 140°
  39. 39.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 15° (c) 105° (d) 75°
  40. 40.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) 20° (d) 160°

Answer key

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

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