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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 99 · 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 95°. What is the angle next to it on the same straight line? (a) 86° (b) 265° (c) 95° (d) 85°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 80° (c) 50° (d) 40°
  3. 3.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 155° (c) 335° (d) 25°
  4. 4.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 120° (d) 155°
  5. 5.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 90° (c) 135° (d) 91°
  6. 6.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 155° (b) 75° (c) 105° (d) 100°
  7. 7.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 270° (b) 150° (c) 90° (d) 120°
  8. 8.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 10° (b) 80° (c) 170° (d) 110°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 130° (c) 50° (d) 100°
  10. 10.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 55° (b) 150° (c) 155° (d) 25°
  11. 11.Two angles of a triangle are 55° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 75° (c) 105° (d) 125°
  12. 12.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 120° (d) 60°
  13. 13.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 155° (c) 60° (d) 145°
  14. 14.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 270° (b) 115° (c) 155° (d) 90°
  15. 15.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 50° (b) 30° (c) 160° (d) 150°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 40° (b) 21° (c) 20° (d) 160°
  17. 17.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 135° (b) 55° (c) 10° (d) 170°
  18. 18.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 75° (b) 15° (c) 120° (d) 165°
  19. 19.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 80° (b) 135° (c) 100° (d) 125°
  20. 20.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 85° (d) 10°
  21. 21.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 260° (b) 100° (c) 80° (d) 160°
  22. 22.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 150° (c) 50° (d) 130°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 190° (c) 10° (d) 95°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 130° (c) 65° (d) 115°
  25. 25.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 160° (b) 270° (c) 110° (d) 90°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 50° (c) 10° (d) 100°
  27. 27.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 100° (c) 80° (d) 20°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 20° (c) 70° (d) 110°
  29. 29.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 160° (b) 20° (c) 150° (d) 50°
  30. 30.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 80° (d) 40°
  31. 31.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 75° (b) 125° (c) 105° (d) 160°
  32. 32.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 65° (c) 140° (d) 105°
  33. 33.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 125° (d) 85°
  34. 34.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 20° (c) 160° (d) 70°
  35. 35.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 160° (b) 120° (c) 80° (d) 20°
  36. 36.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 105° (b) 285° (c) 15° (d) 75°
  37. 37.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 55° (b) 120° (c) 115° (d) 125°
  38. 38.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 40° (b) 115° (c) 105° (d) 140°
  39. 39.Two angles of a triangle are 25° and 75°. What is the third angle? (a) 100° (b) 105° (c) 80° (d) 155°
  40. 40.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 65° (c) 145° (d) 115°

Answer key

  1. 85°
  2. 40°
  3. 155°
  4. 85°
  5. 90°
  6. 75°
  7. 90°
  8. 10°
  9. 50°
  10. 25°
  11. 105°
  12. 120°
  13. 60°
  14. 90°
  15. 150°
  16. 20°
  17. 10°
  18. 15°
  19. 100°
  20. 10°
  21. 100°
  22. 50°
  23. 95°
  24. 65°
  25. 90°
  26. 50°
  27. 20°
  28. 55°
  29. 20°
  30. 80°
  31. 75°
  32. 65°
  33. 85°
  34. 160°
  35. 20°
  36. 105°
  37. 125°
  38. 40°
  39. 80°
  40. 115°

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