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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 117 · 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 25° and 55°. What is the exterior angle at the third corner? (a) 155° (b) 125° (c) 80° (d) 100°
  2. 2.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 55° (b) 235° (c) 56° (d) 125°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 155° (c) 130° (d) 310°
  4. 4.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 91° (b) 135° (c) 270° (d) 90°
  5. 5.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) 160° (c) 20° (d) 21°
  6. 6.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 10° (d) 11°
  7. 7.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 85° (d) 145°
  8. 8.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 155° (b) 75° (c) 130° (d) 105°
  9. 9.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 255° (b) 105° (c) 75° (d) 150°
  10. 10.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 140° (b) 270° (c) 130° (d) 90°
  11. 11.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 320° (c) 40° (d) 140°
  12. 12.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 85° (d) 160°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 110° (c) 55° (d) 70°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 45° (c) 55° (d) 46°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 10° (c) 50° (d) 80°
  16. 16.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 220° (c) 40° (d) 140°
  17. 17.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 75° (b) 125° (c) 130° (d) 105°
  18. 18.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 110° (b) 150° (c) 30° (d) 100°
  19. 19.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 160° (b) 85° (c) 105° (d) 95°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 40° (c) 20° (d) 30°
  21. 21.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 160° (b) 110° (c) 70° (d) 130°
  22. 22.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 140° (c) 50° (d) 40°
  23. 23.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 65° (b) 155° (c) 115° (d) 140°
  24. 24.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 90° (b) 160° (c) 110° (d) 270°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 40° (c) 60° (d) 30°
  26. 26.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 110° (b) 170° (c) 80° (d) 10°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 81° (b) 160° (c) 100° (d) 80°
  28. 28.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 30° (c) 75° (d) 60°
  29. 29.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 65° (c) 66° (d) 115°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 140° (b) 100° (c) 40° (d) 280°
  31. 31.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 110° (b) 105° (c) 35° (d) 145°
  32. 32.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 10° (c) 85° (d) 5°
  33. 33.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 40° (b) 155° (c) 165° (d) 15°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 85° (c) 95° (d) 170°
  35. 35.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 55° (b) 160° (c) 125° (d) 145°
  36. 36.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 26° (c) 205° (d) 25°
  37. 37.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 85° (b) 115° (c) 150° (d) 95°
  38. 38.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 145° (b) 150° (c) 65° (d) 30°
  39. 39.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 45° (b) 95° (c) 130° (d) 135°
  40. 40.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 80° (c) 110° (d) 100°

Answer key

  1. 80°
  2. 55°
  3. 155°
  4. 90°
  5. 20°
  6. 10°
  7. 130°
  8. 75°
  9. 105°
  10. 90°
  11. 40°
  12. 85°
  13. 55°
  14. 45°
  15. 50°
  16. 140°
  17. 105°
  18. 30°
  19. 85°
  20. 20°
  21. 110°
  22. 140°
  23. 65°
  24. 90°
  25. 30°
  26. 10°
  27. 80°
  28. 75°
  29. 65°
  30. 140°
  31. 35°
  32. 10°
  33. 15°
  34. 85°
  35. 125°
  36. 25°
  37. 95°
  38. 30°
  39. 135°
  40. 100°

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