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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 490 · 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 angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 50° (c) 130° (d) 40°
  2. 2.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 50° (b) 230° (c) 130° (d) 100°
  3. 3.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 130° (b) 70° (c) 110° (d) 160°
  4. 4.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 120° (b) 100° (c) 140° (d) 40°
  5. 5.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 105° (c) 30° (d) 75°
  6. 6.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 150° (b) 65° (c) 145° (d) 35°
  7. 7.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 80° (b) 160° (c) 260° (d) 100°
  8. 8.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 30° (b) 125° (c) 150° (d) 85°
  9. 9.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 125° (c) 50° (d) 105°
  10. 10.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 125° (b) 150° (c) 55° (d) 155°
  11. 11.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 160° (b) 45° (c) 20° (d) 155°
  12. 12.Two angles of a triangle are 25° and 75°. What is the third angle? (a) 155° (b) 105° (c) 80° (d) 100°
  13. 13.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 70° (d) 55°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 40° (c) 100° (d) 140°
  15. 15.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°
  16. 16.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 100° (b) 160° (c) 80° (d) 120°
  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) 195° (b) 16° (c) 165° (d) 15°
  18. 18.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 130° (b) 165° (c) 15° (d) 65°
  19. 19.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 300° (b) 120° (c) 150° (d) 60°
  20. 20.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 125° (b) 150° (c) 155° (d) 55°
  21. 21.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 25° (b) 155° (c) 150° (d) 55°
  22. 22.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 50° (c) 25° (d) 65°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 15° (c) 30° (d) 25°
  24. 24.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 105° (b) 75° (c) 255° (d) 150°
  25. 25.Two angles of a triangle are 45° and 80°. What is the third angle? (a) 100° (b) 55° (c) 135° (d) 125°
  26. 26.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 80° (b) 150° (c) 130° (d) 100°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 140° (c) 160° (d) 320°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 61° (c) 60° (d) 59°
  29. 29.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) 70° (d) 55°
  30. 30.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 105° (b) 140° (c) 75° (d) 145°
  31. 31.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 60° (b) 125° (c) 120° (d) 115°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 30° (d) 70°
  33. 33.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 110° (d) 235°
  34. 34.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 160° (c) 95° (d) 105°
  35. 35.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 55° (d) 125°
  36. 36.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 50° (d) 40°
  37. 37.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 160° (b) 75° (c) 55° (d) 125°
  38. 38.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 160° (b) 120° (c) 60° (d) 140°
  39. 39.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 70° (c) 20° (d) 40°
  40. 40.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°

Answer key

  1. 65°
  2. 50°
  3. 70°
  4. 40°
  5. 30°
  6. 35°
  7. 100°
  8. 150°
  9. 130°
  10. 55°
  11. 20°
  12. 80°
  13. 70°
  14. 140°
  15. 35°
  16. 80°
  17. 15°
  18. 15°
  19. 120°
  20. 125°
  21. 25°
  22. 50°
  23. 15°
  24. 75°
  25. 55°
  26. 80°
  27. 160°
  28. 60°
  29. 125°
  30. 105°
  31. 120°
  32. 60°
  33. 125°
  34. 95°
  35. 125°
  36. 100°
  37. 55°
  38. 60°
  39. 40°
  40. 45°

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