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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 16 · 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 angles of a triangle are 65° and 100°. What is the third angle? (a) 165° (b) 15° (c) 80° (d) 115°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 40° (d) 140°
  3. 3.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 145° (b) 75° (c) 105° (d) 140°
  4. 4.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 95° (d) 115°
  5. 5.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 80° (b) 155° (c) 100° (d) 125°
  6. 6.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 80° (b) 160° (c) 120° (d) 60°
  7. 7.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 71° (c) 250° (d) 70°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 45° (c) 35° (d) 110°
  9. 9.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 30° (d) 120°
  10. 10.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 45° (b) 115° (c) 110° (d) 135°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 40° (c) 41° (d) 80°
  12. 12.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 130° (b) 110° (c) 120° (d) 50°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 40° (c) 21° (d) 20°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 240° (c) 120° (d) 121°
  15. 15.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 100° (b) 50° (c) 130° (d) 230°
  16. 16.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 45° (c) 155° (d) 135°
  17. 17.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 125° (b) 100° (c) 80° (d) 135°
  18. 18.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 140° (d) 100°
  19. 19.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 90° (b) 115° (c) 155° (d) 270°
  20. 20.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 80° (c) 100° (d) 20°
  21. 21.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 145° (b) 80° (c) 135° (d) 100°
  22. 22.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) 86° (d) 85°
  23. 23.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 140° (b) 100° (c) 80° (d) 120°
  24. 24.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) 75° (c) 15° (d) 285°
  25. 25.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 55° (b) 160° (c) 35° (d) 145°
  26. 26.Two angles of a triangle are 50° and 55°. What is the third angle? (a) 105° (b) 125° (c) 130° (d) 75°
  27. 27.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 65° (b) 160° (c) 135° (d) 20°
  28. 28.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 160° (b) 100° (c) 80° (d) 260°
  29. 29.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 150° (b) 70° (c) 140° (d) 110°
  30. 30.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 150° (d) 270°
  31. 31.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 120° (d) 105°
  32. 32.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 120° (b) 155° (c) 60° (d) 85°
  33. 33.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 110° (b) 70° (c) 130° (d) 160°
  34. 34.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 115° (b) 140° (c) 40° (d) 105°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 60° (d) 30°
  36. 36.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 70° (d) 110°
  37. 37.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 195° (c) 15° (d) 16°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 50° (d) 25°
  39. 39.Two angles of a triangle are 50° and 100°. What is the third angle? (a) 130° (b) 150° (c) 30° (d) 80°
  40. 40.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 270° (b) 135° (c) 90° (d) 91°

Answer key

  1. 15°
  2. 70°
  3. 105°
  4. 150°
  5. 100°
  6. 60°
  7. 70°
  8. 35°
  9. 60°
  10. 135°
  11. 40°
  12. 50°
  13. 20°
  14. 120°
  15. 50°
  16. 45°
  17. 80°
  18. 120°
  19. 90°
  20. 20°
  21. 80°
  22. 85°
  23. 80°
  24. 105°
  25. 145°
  26. 75°
  27. 20°
  28. 80°
  29. 110°
  30. 90°
  31. 135°
  32. 60°
  33. 110°
  34. 40°
  35. 60°
  36. 40°
  37. 15°
  38. 25°
  39. 30°
  40. 90°

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