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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 423 · 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 40° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 65° (c) 115° (d) 140°
  2. 2.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 85° (b) 95° (c) 115° (d) 160°
  3. 3.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 80° (b) 130° (c) 100° (d) 150°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 100° (c) 50° (d) 80°
  5. 5.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 115° (b) 110° (c) 70° (d) 135°
  6. 6.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 160° (c) 95° (d) 105°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 100° (c) 140° (d) 40°
  8. 8.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 170° (b) 10° (c) 135° (d) 55°
  9. 9.Two angles of a triangle are 20° and 105°. What is the exterior angle at the third corner? (a) 160° (b) 75° (c) 55° (d) 125°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 120° (c) 61° (d) 60°
  11. 11.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 140° (b) 40° (c) 90° (d) 130°
  12. 12.Two angles of a triangle are 50° and 70°. What is the third angle? (a) 120° (b) 110° (c) 60° (d) 130°
  13. 13.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 110° (b) 20° (c) 70° (d) 290°
  14. 14.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 50° (c) 40° (d) 310°
  15. 15.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 145° (c) 125° (d) 55°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 150° (d) 75°
  17. 17.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 120° (b) 150° (c) 90° (d) 270°
  18. 18.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 100° (b) 155° (c) 80° (d) 125°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 70° (d) 35°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 76° (c) 75° (d) 150°
  21. 21.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 245° (c) 65° (d) 115°
  22. 22.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 125° (b) 115° (c) 60° (d) 120°
  23. 23.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 75° (c) 15° (d) 30°
  24. 24.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 120° (b) 135° (c) 105° (d) 60°
  25. 25.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 135° (c) 155° (d) 45°
  26. 26.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 155° (b) 140° (c) 65° (d) 115°
  27. 27.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 65° (b) 10° (c) 170° (d) 125°
  28. 28.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 110° (b) 95° (c) 85° (d) 155°
  29. 29.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 55° (b) 155° (c) 150° (d) 125°
  30. 30.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 105° (d) 145°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 40° (d) 65°
  32. 32.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 140° (b) 150° (c) 70° (d) 110°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 150° (c) 25° (d) 15°
  34. 34.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 200° (c) 20° (d) 160°
  35. 35.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 110° (b) 155° (c) 95° (d) 85°
  36. 36.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 60° (b) 130° (c) 170° (d) 10°
  37. 37.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 70° (c) 215° (d) 35°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 70° (c) 20° (d) 110°
  39. 39.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 160° (c) 270° (d) 90°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 75° (c) 210° (d) 30°

Answer key

  1. 65°
  2. 95°
  3. 100°
  4. 40°
  5. 70°
  6. 95°
  7. 140°
  8. 10°
  9. 125°
  10. 60°
  11. 40°
  12. 60°
  13. 110°
  14. 130°
  15. 125°
  16. 75°
  17. 90°
  18. 100°
  19. 35°
  20. 75°
  21. 115°
  22. 60°
  23. 30°
  24. 120°
  25. 45°
  26. 65°
  27. 10°
  28. 85°
  29. 125°
  30. 110°
  31. 65°
  32. 70°
  33. 15°
  34. 20°
  35. 95°
  36. 10°
  37. 35°
  38. 55°
  39. 90°
  40. 105°

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