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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 414 · 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 45° each. What is the third angle? (a) 90° (b) 45° (c) 91° (d) 135°
  2. 2.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 45° (b) 100° (c) 125° (d) 135°
  3. 3.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 60° (b) 155° (c) 145° (d) 120°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 85° (c) 170° (d) 95°
  5. 5.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 120° (b) 80° (c) 60° (d) 160°
  6. 6.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 325° (d) 55°
  7. 7.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 35° (b) 90° (c) 145° (d) 125°
  8. 8.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 105° (d) 120°
  9. 9.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 130° (b) 120° (c) 110° (d) 70°
  10. 10.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 85° (d) 86°
  11. 11.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 35° (b) 105° (c) 145° (d) 110°
  12. 12.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 65° (b) 115° (c) 140° (d) 155°
  13. 13.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 40° (b) 120° (c) 100° (d) 140°
  14. 14.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) 80° (d) 10°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 130° (c) 80° (d) 260°
  16. 16.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 60° (c) 150° (d) 30°
  17. 17.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 40° (b) 220° (c) 140° (d) 80°
  18. 18.Two angles of a triangle are 35° and 85°. What is the third angle? (a) 60° (b) 120° (c) 95° (d) 145°
  19. 19.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 135° (d) 155°
  20. 20.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 120° (b) 145° (c) 85° (d) 95°
  21. 21.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 95° (d) 5°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 280° (c) 140° (d) 100°
  23. 23.Two angles of a triangle are 25° and 85°. What is the exterior angle at the third corner? (a) 155° (b) 95° (c) 110° (d) 70°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 25° (c) 30° (d) 15°
  25. 25.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 125° (b) 55° (c) 35° (d) 305°
  26. 26.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 155° (d) 110°
  27. 27.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 160° (b) 70° (c) 110° (d) 130°
  28. 28.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 140° (b) 100° (c) 80° (d) 280°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 10° (c) 20° (d) 11°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 10° (c) 85° (d) 95°
  31. 31.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 85° (b) 155° (c) 120° (d) 25°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 60° (c) 40° (d) 120°
  33. 33.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 80° (c) 100° (d) 120°
  34. 34.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 105° (b) 125° (c) 130° (d) 75°
  35. 35.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 30° (d) 15°
  36. 36.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 155° (b) 30° (c) 150° (d) 55°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 150° (c) 75° (d) 30°
  38. 38.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 65° (c) 155° (d) 115°
  39. 39.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 140° (b) 100° (c) 120° (d) 60°
  40. 40.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 80° (c) 50° (d) 40°

Answer key

  1. 90°
  2. 45°
  3. 120°
  4. 85°
  5. 120°
  6. 145°
  7. 35°
  8. 135°
  9. 70°
  10. 85°
  11. 35°
  12. 115°
  13. 140°
  14. 50°
  15. 130°
  16. 120°
  17. 140°
  18. 60°
  19. 70°
  20. 85°
  21. 10°
  22. 140°
  23. 110°
  24. 15°
  25. 125°
  26. 95°
  27. 110°
  28. 100°
  29. 10°
  30. 95°
  31. 25°
  32. 30°
  33. 80°
  34. 105°
  35. 30°
  36. 30°
  37. 75°
  38. 65°
  39. 60°
  40. 80°

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