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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 193 · 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 two equal angles are 60° each. What is the third angle? (a) 120° (b) 61° (c) 60° (d) 30°
  2. 2.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 15° (d) 75°
  3. 3.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 145° (b) 130° (c) 85° (d) 95°
  4. 4.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 135° (b) 95° (c) 85° (d) 140°
  5. 5.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 150° (b) 115° (c) 65° (d) 145°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 40°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 70° (c) 160° (d) 20°
  8. 8.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 300° (c) 30° (d) 120°
  9. 9.Two angles of a triangle are 55° and 95°. What is the third angle? (a) 30° (b) 85° (c) 125° (d) 150°
  10. 10.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 40° (b) 115° (c) 105° (d) 140°
  11. 11.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 150° (b) 20° (c) 160° (d) 50°
  12. 12.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 140° (c) 40° (d) 41°
  13. 13.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 145° (b) 60° (c) 95° (d) 120°
  14. 14.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 115° (c) 245° (d) 65°
  15. 15.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 150° (b) 115° (c) 95° (d) 65°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 81° (c) 100° (d) 160°
  17. 17.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 65° (d) 150°
  18. 18.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 155° (b) 125° (c) 55° (d) 150°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 20° (c) 30° (d) 140°
  20. 20.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 110° (b) 145° (c) 35° (d) 105°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 40° (c) 50° (d) 130°
  22. 22.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 105° (b) 150° (c) 30° (d) 210°
  23. 23.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 105° (c) 160° (d) 75°
  24. 24.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 120° (b) 85° (c) 145° (d) 95°
  25. 25.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 100° (d) 155°
  26. 26.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 95° (c) 85° (d) 10°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 10° (c) 170° (d) 11°
  28. 28.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 55° (d) 125°
  29. 29.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 105° (b) 100° (c) 75° (d) 155°
  30. 30.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 80° (b) 105° (c) 155° (d) 100°
  31. 31.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 115° (b) 295° (c) 65° (d) 25°
  32. 32.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 110° (b) 80° (c) 100° (d) 150°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 270° (c) 135° (d) 45°
  34. 34.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 270° (b) 155° (c) 90° (d) 115°
  35. 35.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 70° (b) 45° (c) 155° (d) 135°
  36. 36.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 110° (b) 130° (c) 120° (d) 70°
  37. 37.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 110° (c) 145° (d) 35°
  38. 38.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 120° (b) 55° (c) 125° (d) 115°
  39. 39.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 140° (d) 60°
  40. 40.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) 200° (c) 21° (d) 160°

Answer key

  1. 60°
  2. 30°
  3. 95°
  4. 95°
  5. 65°
  6. 40°
  7. 80°
  8. 120°
  9. 30°
  10. 140°
  11. 20°
  12. 40°
  13. 60°
  14. 65°
  15. 65°
  16. 80°
  17. 65°
  18. 125°
  19. 20°
  20. 145°
  21. 65°
  22. 30°
  23. 105°
  24. 85°
  25. 105°
  26. 10°
  27. 10°
  28. 125°
  29. 75°
  30. 100°
  31. 115°
  32. 80°
  33. 135°
  34. 90°
  35. 45°
  36. 70°
  37. 110°
  38. 55°
  39. 120°
  40. 20°

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