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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 342 · 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 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 280° (d) 140°
  2. 2.Two angles of a triangle are 20° and 105°. What is the exterior angle at the third corner? (a) 160° (b) 55° (c) 75° (d) 125°
  3. 3.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 80° (d) 125°
  4. 4.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 35° (b) 110° (c) 145° (d) 105°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 15° (c) 30° (d) 165°
  6. 6.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 160° (b) 50° (c) 150° (d) 20°
  7. 7.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 50° (c) 105° (d) 130°
  8. 8.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 115° (b) 125° (c) 65° (d) 120°
  9. 9.Two angles of a triangle are 30° and 70°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 80° (d) 110°
  10. 10.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 55° (d) 155°
  11. 11.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) 75° (d) 150°
  12. 12.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 60° (c) 120° (d) 61°
  13. 13.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) 160° (c) 20° (d) 200°
  14. 14.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 125° (d) 80°
  15. 15.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 55° (d) 125°
  16. 16.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 115° (b) 75° (c) 170° (d) 10°
  17. 17.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 10° (c) 85° (d) 5°
  18. 18.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 35° (c) 145° (d) 110°
  19. 19.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 115° (b) 140° (c) 75° (d) 105°
  20. 20.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 105° (d) 130°
  21. 21.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 80° (d) 20°
  22. 22.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 125° (c) 305° (d) 35°
  23. 23.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 91° (b) 270° (c) 90° (d) 135°
  24. 24.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 95° (c) 85° (d) 160°
  25. 25.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 120° (b) 130° (c) 60° (d) 110°
  26. 26.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 50° (c) 130° (d) 310°
  27. 27.Two angles of a triangle are 50° and 85°. What is the exterior angle at the third corner? (a) 130° (b) 95° (c) 45° (d) 135°
  28. 28.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 75° (b) 30° (c) 150° (d) 135°
  29. 29.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 100° (b) 15° (c) 165° (d) 95°
  30. 30.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 90° (d) 270°
  31. 31.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 120° (d) 105°
  32. 32.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 40° (b) 130° (c) 140° (d) 90°
  33. 33.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 250° (c) 70° (d) 110°
  34. 34.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 125° (b) 45° (c) 135° (d) 100°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 150° (c) 300° (d) 120°
  36. 36.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 115° (b) 65° (c) 145° (d) 100°
  37. 37.Two angles of a triangle are 60° and 55°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 125° (d) 120°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 21° (c) 20° (d) 40°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 90° (b) 135° (c) 45° (d) 46°
  40. 40.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 85° (b) 135° (c) 140° (d) 95°

Answer key

  1. 140°
  2. 125°
  3. 100°
  4. 145°
  5. 15°
  6. 20°
  7. 130°
  8. 65°
  9. 100°
  10. 150°
  11. 75°
  12. 60°
  13. 20°
  14. 100°
  15. 125°
  16. 10°
  17. 10°
  18. 145°
  19. 75°
  20. 125°
  21. 20°
  22. 125°
  23. 90°
  24. 95°
  25. 60°
  26. 130°
  27. 135°
  28. 30°
  29. 15°
  30. 90°
  31. 135°
  32. 40°
  33. 70°
  34. 45°
  35. 150°
  36. 65°
  37. 115°
  38. 20°
  39. 45°
  40. 85°

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