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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 397 · 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 75° each. What is the third angle? (a) 105° (b) 75° (c) 15° (d) 30°
  2. 2.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) 20° (c) 160° (d) 200°
  3. 3.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) 16° (d) 15°
  4. 4.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 110° (d) 145°
  5. 5.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 70° (b) 135° (c) 25° (d) 155°
  6. 6.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 30° (c) 150° (d) 120°
  7. 7.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 15° (b) 80° (c) 165° (d) 115°
  8. 8.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 120° (b) 115° (c) 65° (d) 125°
  9. 9.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 125° (b) 95° (c) 85° (d) 150°
  10. 10.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) 45° (d) 110°
  11. 11.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 145° (d) 65°
  12. 12.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 155° (b) 95° (c) 85° (d) 120°
  13. 13.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 95° (d) 135°
  14. 14.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 110° (b) 70° (c) 145° (d) 290°
  15. 15.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 160° (c) 80° (d) 260°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 60° (c) 150° (d) 75°
  17. 17.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 80° (b) 115° (c) 100° (d) 145°
  18. 18.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 140° (c) 155° (d) 65°
  19. 19.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 105° (b) 125° (c) 130° (d) 55°
  20. 20.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 140° (b) 45° (c) 85° (d) 135°
  21. 21.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 155° (b) 130° (c) 50° (d) 310°
  22. 22.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°
  23. 23.Two angles of a triangle are 50° and 50°. What is the exterior angle at the third corner? (a) 80° (b) 260° (c) 130° (d) 100°
  24. 24.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 155° (b) 80° (c) 100° (d) 105°
  25. 25.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 130° (b) 90° (c) 140° (d) 50°
  26. 26.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 55° (c) 325° (d) 145°
  27. 27.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 105° (b) 255° (c) 150° (d) 75°
  28. 28.Two angles of a triangle are 25° and 60°. What is the third angle? (a) 95° (b) 85° (c) 155° (d) 120°
  29. 29.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 105° (b) 160° (c) 95° (d) 20°
  30. 30.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 110° (b) 115° (c) 135° (d) 70°
  31. 31.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°
  32. 32.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 40° (b) 140° (c) 100° (d) 120°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 30° (c) 210° (d) 105°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 75° (b) 76° (c) 105° (d) 150°
  35. 35.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 155° (b) 80° (c) 25° (d) 125°
  36. 36.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 25° (b) 155° (c) 105° (d) 100°
  37. 37.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 135° (b) 155° (c) 70° (d) 45°
  38. 38.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 125° (b) 145° (c) 35° (d) 90°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 15° (b) 25° (c) 30° (d) 150°
  40. 40.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 66° (c) 65° (d) 245°

Answer key

  1. 30°
  2. 20°
  3. 15°
  4. 110°
  5. 25°
  6. 120°
  7. 15°
  8. 65°
  9. 85°
  10. 35°
  11. 115°
  12. 95°
  13. 130°
  14. 110°
  15. 100°
  16. 75°
  17. 80°
  18. 65°
  19. 55°
  20. 45°
  21. 130°
  22. 65°
  23. 100°
  24. 80°
  25. 50°
  26. 145°
  27. 105°
  28. 95°
  29. 20°
  30. 70°
  31. 45°
  32. 40°
  33. 105°
  34. 75°
  35. 25°
  36. 25°
  37. 45°
  38. 35°
  39. 15°
  40. 65°

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