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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 112 · 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.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 35° (c) 125° (d) 55°
  2. 2.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 45° (b) 145° (c) 80° (d) 135°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 160° (d) 80°
  4. 4.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) 135° (c) 315° (d) 45°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 20° (c) 70° (d) 110°
  6. 6.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 100° (d) 145°
  7. 7.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 110° (b) 55° (c) 235° (d) 125°
  8. 8.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 110° (d) 70°
  9. 9.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 155° (b) 75° (c) 105° (d) 100°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 50° (c) 155° (d) 25°
  11. 11.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 115° (b) 135° (c) 45° (d) 110°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 160° (c) 20° (d) 10°
  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) 215° (b) 36° (c) 145° (d) 35°
  14. 14.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 130° (b) 135° (c) 95° (d) 85°
  15. 15.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 145° (b) 140° (c) 75° (d) 105°
  16. 16.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 30° (b) 210° (c) 150° (d) 105°
  17. 17.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 130° (d) 65°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 40° (b) 80° (c) 140° (d) 41°
  19. 19.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 80° (c) 10° (d) 100°
  20. 20.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 130° (d) 155°
  21. 21.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 140° (b) 150° (c) 110° (d) 70°
  22. 22.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 105° (b) 110° (c) 145° (d) 35°
  23. 23.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 25° (d) 50°
  24. 24.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 145° (b) 135° (c) 100° (d) 80°
  25. 25.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 60° (c) 120° (d) 140°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 50° (c) 140° (d) 70°
  27. 27.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 20° (c) 200° (d) 160°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 60° (d) 30°
  29. 29.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 10° (b) 85° (c) 170° (d) 105°
  30. 30.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 50° (c) 130° (d) 40°
  31. 31.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 120° (b) 95° (c) 155° (d) 85°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 30° (c) 40° (d) 140°
  33. 33.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 160° (b) 135° (c) 115° (d) 65°
  34. 34.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 95° (c) 10° (d) 5°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 30° (c) 25° (d) 15°
  36. 36.Two angles of a triangle are 20° and 120°. What is the exterior angle at the third corner? (a) 140° (b) 60° (c) 160° (d) 40°
  37. 37.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 20° (c) 110° (d) 70°
  38. 38.Two angles of a triangle are 20° and 110°. What is the exterior angle at the third corner? (a) 130° (b) 70° (c) 50° (d) 160°
  39. 39.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 270° (c) 90° (d) 155°
  40. 40.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 125° (b) 120° (c) 115° (d) 55°

Answer key

  1. 70°
  2. 135°
  3. 80°
  4. 135°
  5. 55°
  6. 115°
  7. 55°
  8. 110°
  9. 75°
  10. 25°
  11. 45°
  12. 10°
  13. 35°
  14. 85°
  15. 75°
  16. 150°
  17. 130°
  18. 40°
  19. 20°
  20. 75°
  21. 110°
  22. 35°
  23. 50°
  24. 80°
  25. 120°
  26. 70°
  27. 20°
  28. 60°
  29. 10°
  30. 80°
  31. 95°
  32. 20°
  33. 65°
  34. 10°
  35. 15°
  36. 140°
  37. 40°
  38. 130°
  39. 90°
  40. 55°

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