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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 848 · 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 30° and 30°. What is the exterior angle at the third corner? (a) 120° (b) 150° (c) 60° (d) 300°
  2. 2.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 310° (b) 155° (c) 130° (d) 50°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 70° (c) 110° (d) 45°
  4. 4.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 25° (c) 65° (d) 115°
  5. 5.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 100° (b) 115° (c) 35° (d) 145°
  6. 6.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 150° (c) 60° (d) 330°
  7. 7.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 145° (c) 130° (d) 95°
  8. 8.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) 95° (c) 265° (d) 85°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 30° (c) 150° (d) 60°
  10. 10.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 40° (b) 15° (c) 155° (d) 165°
  11. 11.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 30° (c) 75° (d) 105°
  12. 12.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 135° (b) 10° (c) 55° (d) 170°
  13. 13.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 85° (b) 95° (c) 115° (d) 160°
  14. 14.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 30° (c) 150° (d) 115°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 130° (c) 50° (d) 35°
  16. 16.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 260° (d) 130°
  17. 17.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 250° (c) 110° (d) 71°
  18. 18.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 120° (b) 130° (c) 110° (d) 70°
  19. 19.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 21° (c) 160° (d) 20°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 30° (c) 40° (d) 120°
  21. 21.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 150° (d) 85°
  22. 22.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 120° (d) 100°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 80° (d) 20°
  24. 24.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 145° (d) 35°
  25. 25.Two angles of a triangle are 60° and 60°. What is the exterior angle at the third corner? (a) 121° (b) 240° (c) 120° (d) 60°
  26. 26.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 55° (b) 115° (c) 125° (d) 120°
  27. 27.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 75° (b) 160° (c) 55° (d) 125°
  28. 28.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 135° (b) 85° (c) 140° (d) 95°
  29. 29.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 135° (b) 115° (c) 70° (d) 110°
  30. 30.Two angles of a triangle are 20° and 60°. What is the third angle? (a) 80° (b) 100° (c) 120° (d) 160°
  31. 31.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 125° (d) 70°
  32. 32.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 90° (c) 270° (d) 125°
  33. 33.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 170° (b) 10° (c) 160° (d) 30°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 70° (c) 110° (d) 220°
  35. 35.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 215° (c) 70° (d) 35°
  36. 36.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 51° (b) 230° (c) 130° (d) 50°
  37. 37.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 105° (b) 40° (c) 115° (d) 140°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 90° (c) 46° (d) 45°
  39. 39.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 35° (d) 55°
  40. 40.Two angles of a triangle are 20° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 135° (c) 45° (d) 160°

Answer key

  1. 60°
  2. 130°
  3. 35°
  4. 115°
  5. 35°
  6. 150°
  7. 85°
  8. 85°
  9. 75°
  10. 15°
  11. 30°
  12. 10°
  13. 95°
  14. 150°
  15. 25°
  16. 100°
  17. 70°
  18. 110°
  19. 20°
  20. 30°
  21. 95°
  22. 140°
  23. 80°
  24. 145°
  25. 120°
  26. 125°
  27. 55°
  28. 85°
  29. 70°
  30. 100°
  31. 70°
  32. 90°
  33. 10°
  34. 110°
  35. 35°
  36. 50°
  37. 40°
  38. 45°
  39. 110°
  40. 135°

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