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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 81 · 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 straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 75° (c) 105° (d) 76°
  2. 2.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 50° (b) 160° (c) 130° (d) 150°
  3. 3.Two angles of a triangle are 40° and 70°. What is the third angle? (a) 250° (b) 110° (c) 70° (d) 140°
  4. 4.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°
  5. 5.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 136° (b) 315° (c) 135° (d) 45°
  6. 6.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 100° (d) 150°
  7. 7.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) 160° (c) 21° (d) 200°
  8. 8.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 95° (b) 110° (c) 155° (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) 150° (b) 60° (c) 30° (d) 75°
  10. 10.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 36° (b) 215° (c) 35° (d) 145°
  11. 11.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 335° (c) 155° (d) 25°
  12. 12.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 60° (c) 150° (d) 30°
  13. 13.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 150° (d) 75°
  14. 14.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 115° (d) 105°
  15. 15.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 100° (d) 50°
  16. 16.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 140° (b) 95° (c) 125° (d) 40°
  17. 17.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 100° (d) 45°
  18. 18.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 95° (b) 150° (c) 65° (d) 115°
  19. 19.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 95° (c) 86° (d) 85°
  20. 20.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 80° (b) 125° (c) 100° (d) 135°
  21. 21.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 90° (b) 155° (c) 270° (d) 115°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 80° (c) 20° (d) 100°
  23. 23.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 145° (b) 110° (c) 75° (d) 105°
  24. 24.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 150° (b) 100° (c) 80° (d) 130°
  25. 25.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 75° (b) 170° (c) 10° (d) 115°
  26. 26.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 40° (c) 140° (d) 320°
  27. 27.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 65° (c) 115° (d) 245°
  28. 28.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 40° (c) 50° (d) 130°
  29. 29.Two angles of a triangle are 55° and 95°. What is the third angle? (a) 85° (b) 30° (c) 150° (d) 125°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 40° (c) 100° (d) 140°
  31. 31.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 100° (b) 125° (c) 135° (d) 55°
  32. 32.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 220° (b) 110° (c) 140° (d) 40°
  33. 33.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 85° (b) 115° (c) 150° (d) 95°
  34. 34.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°
  35. 35.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 120° (d) 140°
  36. 36.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 110° (b) 70° (c) 125° (d) 250°
  37. 37.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 30° (c) 15° (d) 105°
  38. 38.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 81° (b) 80° (c) 260° (d) 100°
  39. 39.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 150° (b) 160° (c) 130° (d) 50°
  40. 40.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 35° (d) 100°

Answer key

  1. 75°
  2. 50°
  3. 70°
  4. 15°
  5. 135°
  6. 110°
  7. 20°
  8. 85°
  9. 75°
  10. 35°
  11. 155°
  12. 120°
  13. 135°
  14. 105°
  15. 100°
  16. 40°
  17. 135°
  18. 65°
  19. 85°
  20. 100°
  21. 90°
  22. 100°
  23. 75°
  24. 100°
  25. 10°
  26. 140°
  27. 65°
  28. 80°
  29. 30°
  30. 140°
  31. 55°
  32. 40°
  33. 85°
  34. 65°
  35. 100°
  36. 70°
  37. 30°
  38. 80°
  39. 130°
  40. 145°

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