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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 631 · 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 65° each. What is the third angle? (a) 65° (b) 50° (c) 25° (d) 115°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 70° (c) 160° (d) 20°
  3. 3.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 60° (d) 120°
  4. 4.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 46° (b) 135° (c) 225° (d) 45°
  5. 5.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°
  6. 6.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 100° (b) 70° (c) 110° (d) 150°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 30° (c) 150° (d) 60°
  8. 8.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 80° (b) 100° (c) 125° (d) 155°
  9. 9.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 51° (c) 50° (d) 130°
  10. 10.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 5° (c) 275° (d) 95°
  11. 11.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 100° (b) 25° (c) 155° (d) 105°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 55° (b) 56° (c) 125° (d) 110°
  13. 13.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 165° (c) 15° (d) 195°
  14. 14.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 30° (d) 15°
  15. 15.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 70° (d) 110°
  16. 16.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 120° (d) 100°
  17. 17.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 60° (c) 120° (d) 155°
  18. 18.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 85° (b) 95° (c) 155° (d) 110°
  19. 19.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 155° (d) 110°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 60° (c) 120° (d) 59°
  21. 21.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 155° (b) 140° (c) 65° (d) 40°
  22. 22.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 20° (c) 100° (d) 80°
  23. 23.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 65° (b) 115° (c) 145° (d) 100°
  24. 24.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 85° (c) 95° (d) 86°
  25. 25.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 150° (b) 95° (c) 115° (d) 85°
  26. 26.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 95° (b) 110° (c) 155° (d) 25°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 35° (c) 70° (d) 45°
  28. 28.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 65° (b) 155° (c) 25° (d) 140°
  29. 29.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 80° (b) 100° (c) 130° (d) 150°
  30. 30.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 50° (c) 100° (d) 40°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 20° (c) 11° (d) 160°
  32. 32.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 120° (b) 60° (c) 240° (d) 61°
  33. 33.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 105° (b) 125° (c) 50° (d) 130°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 125° (c) 55° (d) 70°
  35. 35.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 160° (b) 110° (c) 90° (d) 20°
  36. 36.Two angles of a triangle are 55° and 95°. What is the third angle? (a) 125° (b) 150° (c) 30° (d) 85°
  37. 37.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 245° (d) 130°
  38. 38.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 160° (d) 155°
  39. 39.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 41° (c) 220° (d) 140°
  40. 40.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 145° (b) 110° (c) 105° (d) 35°

Answer key

  1. 50°
  2. 80°
  3. 120°
  4. 45°
  5. 40°
  6. 70°
  7. 75°
  8. 100°
  9. 50°
  10. 95°
  11. 25°
  12. 55°
  13. 15°
  14. 30°
  15. 40°
  16. 140°
  17. 60°
  18. 85°
  19. 95°
  20. 60°
  21. 40°
  22. 20°
  23. 65°
  24. 85°
  25. 85°
  26. 25°
  27. 35°
  28. 25°
  29. 100°
  30. 100°
  31. 10°
  32. 60°
  33. 50°
  34. 125°
  35. 20°
  36. 30°
  37. 115°
  38. 45°
  39. 40°
  40. 35°

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