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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 176 · 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 80° and 45°. What is the third angle? (a) 125° (b) 100° (c) 55° (d) 135°
  2. 2.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 85° (b) 120° (c) 95° (d) 155°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 140° (c) 40° (d) 50°
  4. 4.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 120° (c) 60° (d) 61°
  5. 5.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) 86° (c) 85° (d) 265°
  6. 6.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 40° (d) 100°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 75° (c) 76° (d) 105°
  8. 8.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 81° (c) 100° (d) 260°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 30° (c) 165° (d) 16°
  10. 10.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 75° (b) 160° (c) 95° (d) 105°
  11. 11.Two angles of a triangle are 30° and 120°. What is the third angle? (a) 30° (b) 210° (c) 150° (d) 60°
  12. 12.Two angles of a triangle are 25° and 90°. What is the third angle? (a) 115° (b) 155° (c) 90° (d) 65°
  13. 13.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 85° (c) 155° (d) 95°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 46° (b) 135° (c) 90° (d) 45°
  15. 15.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 125° (b) 155° (c) 55° (d) 150°
  16. 16.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 140° (b) 220° (c) 41° (d) 40°
  17. 17.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 110° (b) 75° (c) 145° (d) 105°
  18. 18.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°
  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) 20° (b) 21° (c) 200° (d) 160°
  20. 20.Two angles of a triangle are 40° and 75°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 115° (d) 65°
  21. 21.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 130° (b) 95° (c) 145° (d) 85°
  22. 22.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 135° (b) 130° (c) 95° (d) 50°
  23. 23.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 115° (b) 155° (c) 90° (d) 270°
  24. 24.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 95° (b) 275° (c) 5° (d) 85°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 100° (c) 50° (d) 130°
  26. 26.Two angles of a triangle are 45° and 100°. What is the third angle? (a) 35° (b) 135° (c) 145° (d) 80°
  27. 27.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 145° (b) 140° (c) 105° (d) 75°
  28. 28.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 125° (c) 55° (d) 35°
  29. 29.Two angles of a triangle are 50° and 100°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 130° (d) 80°
  30. 30.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 65° (d) 130°
  31. 31.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 150° (d) 120°
  32. 32.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 65° (c) 140° (d) 115°
  33. 33.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 50° (b) 130° (c) 230° (d) 51°
  34. 34.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 220° (b) 140° (c) 40° (d) 110°
  35. 35.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 65° (b) 125° (c) 120° (d) 115°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 120° (c) 40° (d) 30°
  37. 37.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) 66° (c) 115° (d) 65°
  38. 38.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 70° (c) 20° (d) 340°
  39. 39.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 155° (b) 70° (c) 110° (d) 135°
  40. 40.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 90° (d) 160°

Answer key

  1. 55°
  2. 85°
  3. 70°
  4. 60°
  5. 85°
  6. 100°
  7. 75°
  8. 80°
  9. 15°
  10. 75°
  11. 30°
  12. 65°
  13. 95°
  14. 45°
  15. 125°
  16. 40°
  17. 75°
  18. 130°
  19. 20°
  20. 115°
  21. 95°
  22. 50°
  23. 90°
  24. 95°
  25. 50°
  26. 35°
  27. 105°
  28. 70°
  29. 150°
  30. 130°
  31. 90°
  32. 65°
  33. 50°
  34. 140°
  35. 65°
  36. 30°
  37. 65°
  38. 160°
  39. 110°
  40. 110°

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