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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 900 · 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 160°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 21° (d) 200°
  2. 2.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 150° (b) 60° (c) 90° (d) 120°
  3. 3.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 45° (b) 75° (c) 150° (d) 135°
  4. 4.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 160° (b) 110° (c) 70° (d) 90°
  5. 5.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) 240° (c) 61° (d) 60°
  6. 6.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 105° (b) 155° (c) 100° (d) 75°
  7. 7.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 140° (b) 135° (c) 85° (d) 95°
  8. 8.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 320° (b) 40° (c) 140° (d) 160°
  9. 9.Two angles of a triangle are 40° and 30°. What is the third angle? (a) 140° (b) 70° (c) 110° (d) 150°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 95° (c) 10° (d) 190°
  11. 11.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 65° (d) 335°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 30° (d) 150°
  13. 13.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 60° (b) 115° (c) 120° (d) 125°
  14. 14.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 80° (d) 40°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 40° (d) 65°
  16. 16.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) 150° (d) 30°
  17. 17.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 80° (d) 150°
  18. 18.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 45° (c) 135° (d) 90°
  19. 19.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 245° (c) 65° (d) 115°
  20. 20.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 30° (b) 150° (c) 210° (d) 60°
  21. 21.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 100° (c) 80° (d) 150°
  22. 22.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 61°
  23. 23.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 65° (b) 245° (c) 130° (d) 115°
  24. 24.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 150° (c) 55° (d) 125°
  25. 25.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 160° (b) 115° (c) 65° (d) 85°
  26. 26.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) 120° (d) 60°
  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) 260° (b) 81° (c) 80° (d) 100°
  28. 28.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 150° (c) 30° (d) 330°
  29. 29.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 280° (c) 100° (d) 140°
  30. 30.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 130° (d) 95°
  31. 31.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 155° (b) 160° (c) 135° (d) 45°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 290° (b) 110° (c) 35° (d) 145°
  33. 33.Two angles of a triangle are 50° and 45°. What is the exterior angle at the third corner? (a) 95° (b) 135° (c) 130° (d) 85°
  34. 34.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 150° (b) 160° (c) 50° (d) 130°
  35. 35.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 80° (b) 150° (c) 110° (d) 100°
  36. 36.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 90° (d) 35°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 40°
  38. 38.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 90° (b) 30° (c) 150° (d) 120°
  39. 39.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 145° (b) 50° (c) 165° (d) 15°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 75° (c) 105° (d) 150°

Answer key

  1. 20°
  2. 120°
  3. 135°
  4. 70°
  5. 60°
  6. 75°
  7. 95°
  8. 140°
  9. 110°
  10. 95°
  11. 155°
  12. 15°
  13. 120°
  14. 80°
  15. 65°
  16. 75°
  17. 130°
  18. 90°
  19. 115°
  20. 30°
  21. 80°
  22. 60°
  23. 65°
  24. 125°
  25. 115°
  26. 60°
  27. 80°
  28. 150°
  29. 80°
  30. 135°
  31. 45°
  32. 145°
  33. 95°
  34. 130°
  35. 80°
  36. 145°
  37. 40°
  38. 30°
  39. 15°
  40. 75°

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