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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 76 · 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 120°. What is the angle next to it on the same straight line? (a) 61° (b) 120° (c) 240° (d) 60°
  2. 2.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 140° (b) 110° (c) 70° (d) 150°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 60° (c) 30° (d) 150°
  4. 4.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 60° (b) 120° (c) 125° (d) 115°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 10° (c) 80° (d) 50°
  6. 6.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 65°
  7. 7.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 25° (b) 205° (c) 155° (d) 26°
  8. 8.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 145° (d) 75°
  9. 9.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 140° (b) 65° (c) 155° (d) 40°
  10. 10.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 110° (b) 55° (c) 235° (d) 125°
  11. 11.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 110° (b) 250° (c) 70° (d) 140°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 30° (c) 165° (d) 16°
  13. 13.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 10° (b) 280° (c) 100° (d) 80°
  14. 14.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 150° (b) 55° (c) 155° (d) 125°
  15. 15.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 10° (d) 85°
  16. 16.Two angles of a triangle are 40° and 110°. What is the third angle? (a) 150° (b) 140° (c) 30° (d) 70°
  17. 17.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 150° (b) 145° (c) 65° (d) 30°
  18. 18.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 40° (d) 140°
  19. 19.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 50° (c) 130° (d) 40°
  20. 20.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 70° (d) 40°
  21. 21.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 105° (b) 140° (c) 115° (d) 40°
  22. 22.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 130° (b) 125° (c) 105° (d) 75°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 11° (d) 10°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 110° (c) 125° (d) 55°
  25. 25.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 110° (d) 35°
  26. 26.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 125° (d) 145°
  27. 27.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 145° (d) 130°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 50° (b) 130° (c) 51° (d) 100°
  29. 29.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 65° (c) 115° (d) 155°
  30. 30.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 100° (b) 80° (c) 145° (d) 115°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 140° (c) 50° (d) 40°
  32. 32.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 165° (b) 40° (c) 15° (d) 155°
  33. 33.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 160° (b) 130° (c) 50° (d) 150°
  34. 34.Two angles of a triangle are 50° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 130° (c) 85° (d) 95°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 90° (b) 45° (c) 46° (d) 135°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 110° (b) 220° (c) 70° (d) 40°
  37. 37.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 80° (b) 220° (c) 140° (d) 40°
  38. 38.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 135° (c) 65° (d) 160°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 300° (c) 30° (d) 150°
  40. 40.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 65° (b) 170° (c) 10° (d) 125°

Answer key

  1. 60°
  2. 70°
  3. 75°
  4. 60°
  5. 50°
  6. 130°
  7. 25°
  8. 75°
  9. 140°
  10. 55°
  11. 70°
  12. 15°
  13. 100°
  14. 125°
  15. 10°
  16. 30°
  17. 30°
  18. 100°
  19. 80°
  20. 40°
  21. 40°
  22. 105°
  23. 10°
  24. 55°
  25. 110°
  26. 90°
  27. 85°
  28. 50°
  29. 65°
  30. 80°
  31. 70°
  32. 15°
  33. 130°
  34. 95°
  35. 45°
  36. 110°
  37. 40°
  38. 65°
  39. 150°
  40. 10°

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