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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 5 · 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. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 170° (c) 86° (d) 95°
  2. 2.Two angles of a triangle are 20° and 120°. What is the exterior angle at the third corner? (a) 160° (b) 60° (c) 40° (d) 140°
  3. 3.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 120° (b) 65° (c) 125° (d) 115°
  4. 4.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 10° (b) 45° (c) 145° (d) 170°
  5. 5.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 90° (b) 110° (c) 160° (d) 20°
  6. 6.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) 10° (c) 100° (d) 280°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 55° (c) 45° (d) 90°
  8. 8.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 115° (b) 120° (c) 125° (d) 55°
  9. 9.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 20° (b) 160° (c) 105° (d) 95°
  10. 10.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 75° (b) 145° (c) 105° (d) 140°
  11. 11.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 160° (c) 70° (d) 130°
  12. 12.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 105° (b) 115° (c) 40° (d) 140°
  13. 13.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 140° (b) 95° (c) 85° (d) 135°
  14. 14.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 125° (b) 120° (c) 115° (d) 65°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 30° (c) 20° (d) 140°
  16. 16.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 130° (b) 110° (c) 70° (d) 160°
  17. 17.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 90° (b) 165° (c) 15° (d) 105°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 110° (c) 45° (d) 35°
  19. 19.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 105° (b) 110° (c) 145° (d) 75°
  20. 20.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 50° (d) 115°
  21. 21.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 100° (b) 155° (c) 105° (d) 25°
  22. 22.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 145° (b) 65° (c) 115° (d) 150°
  23. 23.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 60° (b) 61° (c) 240° (d) 120°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 100° (c) 10° (d) 80°
  25. 25.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 150°
  26. 26.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°
  27. 27.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°
  28. 28.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 110° (b) 70° (c) 145° (d) 105°
  29. 29.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 90° (b) 125° (c) 145° (d) 270°
  30. 30.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 80° (b) 15° (c) 165° (d) 115°
  31. 31.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 40° (c) 50° (d) 140°
  32. 32.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 115° (b) 145° (c) 150° (d) 65°
  33. 33.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 125° (d) 80°
  34. 34.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 150° (b) 90° (c) 120° (d) 30°
  35. 35.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 90° (c) 125° (d) 270°
  36. 36.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) 130° (d) 35°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 36° (b) 145° (c) 70° (d) 35°
  38. 38.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 130° (b) 55° (c) 125° (d) 105°
  39. 39.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 125° (c) 75° (d) 105°
  40. 40.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 120° (b) 140° (c) 60° (d) 100°

Answer key

  1. 85°
  2. 140°
  3. 115°
  4. 10°
  5. 20°
  6. 100°
  7. 45°
  8. 55°
  9. 20°
  10. 105°
  11. 70°
  12. 40°
  13. 95°
  14. 115°
  15. 20°
  16. 110°
  17. 15°
  18. 35°
  19. 75°
  20. 50°
  21. 25°
  22. 115°
  23. 60°
  24. 50°
  25. 120°
  26. 65°
  27. 115°
  28. 70°
  29. 90°
  30. 15°
  31. 100°
  32. 115°
  33. 100°
  34. 150°
  35. 90°
  36. 25°
  37. 35°
  38. 55°
  39. 75°
  40. 60°

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