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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 474 · 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 angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 90° (c) 270° (d) 130°
  2. 2.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 135° (b) 45° (c) 136° (d) 315°
  3. 3.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 80° (b) 160° (c) 60° (d) 120°
  4. 4.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 125° (b) 145° (c) 270° (d) 90°
  5. 5.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 230° (b) 50° (c) 100° (d) 130°
  6. 6.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 10° (d) 5°
  7. 7.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 140° (b) 40° (c) 60° (d) 160°
  8. 8.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 130° (c) 75° (d) 155°
  9. 9.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 70° (b) 110° (c) 130° (d) 120°
  10. 10.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 95° (d) 60°
  11. 11.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 56° (c) 55° (d) 235°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 20° (c) 160° (d) 320°
  13. 13.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 90° (b) 270° (c) 91° (d) 135°
  14. 14.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 50° (b) 115° (c) 230° (d) 130°
  15. 15.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 100° (b) 135° (c) 45° (d) 125°
  16. 16.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) 115° (c) 66° (d) 245°
  17. 17.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 16° (c) 165° (d) 195°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 130° (c) 65° (d) 40°
  19. 19.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 80° (c) 260° (d) 100°
  20. 20.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 145° (b) 140° (c) 75° (d) 105°
  21. 21.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 110° (d) 60°
  22. 22.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 50° (b) 230° (c) 100° (d) 130°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 90° (c) 135° (d) 46°
  24. 24.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 75° (b) 105° (c) 150° (d) 255°
  25. 25.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 65° (d) 155°
  26. 26.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 80° (b) 115° (c) 145° (d) 100°
  27. 27.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 40° (d) 70°
  28. 28.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 160° (b) 60° (c) 120° (d) 80°
  29. 29.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 50° (d) 115°
  30. 30.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 125° (c) 55° (d) 105°
  31. 31.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 80° (d) 100°
  32. 32.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 125° (b) 120° (c) 55° (d) 115°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 165° (c) 16° (d) 15°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 75° (c) 150° (d) 30°
  35. 35.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 80° (b) 120° (c) 160° (d) 100°
  36. 36.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 155° (b) 115° (c) 270° (d) 90°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 220° (c) 110° (d) 70°
  38. 38.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 55° (b) 125° (c) 110° (d) 235°
  39. 39.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 270° (b) 155° (c) 90° (d) 115°
  40. 40.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 80° (b) 125° (c) 155° (d) 100°

Answer key

  1. 90°
  2. 135°
  3. 60°
  4. 90°
  5. 130°
  6. 10°
  7. 40°
  8. 75°
  9. 70°
  10. 120°
  11. 55°
  12. 160°
  13. 90°
  14. 130°
  15. 45°
  16. 65°
  17. 15°
  18. 65°
  19. 100°
  20. 105°
  21. 120°
  22. 50°
  23. 45°
  24. 75°
  25. 130°
  26. 100°
  27. 40°
  28. 120°
  29. 50°
  30. 125°
  31. 80°
  32. 55°
  33. 15°
  34. 75°
  35. 80°
  36. 90°
  37. 110°
  38. 55°
  39. 90°
  40. 100°

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