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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 575 · 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 25° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 155° (c) 60° (d) 120°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 75° (b) 105° (c) 150° (d) 76°
  3. 3.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 45° (d) 100°
  4. 4.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 75° (d) 100°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 170° (b) 11° (c) 10° (d) 20°
  6. 6.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 75° (d) 110°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 46° (c) 55° (d) 90°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 40° (c) 21° (d) 20°
  9. 9.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 65° (b) 160° (c) 20° (d) 135°
  10. 10.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 270° (c) 90° (d) 110°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 30° (d) 75°
  12. 12.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 125° (c) 55° (d) 35°
  13. 13.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 125° (d) 55°
  14. 14.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 160° (b) 260° (c) 80° (d) 100°
  15. 15.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 20° (c) 160° (d) 21°
  16. 16.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 165° (b) 95° (c) 100° (d) 15°
  17. 17.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 105° (d) 125°
  18. 18.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 80° (c) 100° (d) 10°
  19. 19.Two angles of a triangle are 60° and 60°. What is the exterior angle at the third corner? (a) 240° (b) 120° (c) 121° (d) 60°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 20° (c) 320° (d) 140°
  21. 21.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 135° (d) 150°
  22. 22.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 150° (b) 210° (c) 105° (d) 30°
  23. 23.Two angles of a triangle are 35° and 115°. What is the exterior angle at the third corner? (a) 145° (b) 30° (c) 150° (d) 65°
  24. 24.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 135° (b) 140° (c) 95° (d) 85°
  25. 25.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 100° (b) 45° (c) 135° (d) 125°
  26. 26.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 80° (b) 120° (c) 100° (d) 140°
  27. 27.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 81° (d) 260°
  28. 28.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 160° (b) 30° (c) 50° (d) 150°
  29. 29.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 100° (c) 40° (d) 140°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 30° (c) 60° (d) 120°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 50° (c) 10° (d) 80°
  32. 32.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 90° (b) 125° (c) 35° (d) 145°
  33. 33.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 125° (b) 270° (c) 90° (d) 145°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 11° (c) 10° (d) 20°
  35. 35.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 115° (b) 55° (c) 125° (d) 120°
  36. 36.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 100° (d) 145°
  37. 37.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 100° (d) 55°
  38. 38.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 50° (b) 230° (c) 115° (d) 130°
  39. 39.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 110° (b) 100° (c) 150° (d) 70°
  40. 40.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 105° (b) 100° (c) 25° (d) 155°

Answer key

  1. 120°
  2. 75°
  3. 135°
  4. 105°
  5. 10°
  6. 105°
  7. 45°
  8. 20°
  9. 20°
  10. 90°
  11. 75°
  12. 70°
  13. 125°
  14. 100°
  15. 20°
  16. 15°
  17. 130°
  18. 20°
  19. 120°
  20. 160°
  21. 75°
  22. 150°
  23. 150°
  24. 95°
  25. 45°
  26. 80°
  27. 80°
  28. 30°
  29. 100°
  30. 60°
  31. 50°
  32. 35°
  33. 90°
  34. 10°
  35. 125°
  36. 115°
  37. 125°
  38. 50°
  39. 70°
  40. 25°

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