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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 61 · 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 35° and 25°. What is the third angle? (a) 60° (b) 155° (c) 145° (d) 120°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 270° (c) 135° (d) 45°
  3. 3.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 270° (c) 110° (d) 90°
  4. 4.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 105° (b) 145° (c) 35° (d) 110°
  5. 5.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 145° (b) 270° (c) 125° (d) 90°
  6. 6.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 115° (c) 50° (d) 65°
  7. 7.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 110° (c) 135° (d) 115°
  8. 8.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 60° (b) 59° (c) 120° (d) 61°
  9. 9.Two angles of a triangle are 25° and 20°. What is the third angle? (a) 45° (b) 160° (c) 155° (d) 135°
  10. 10.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 115° (b) 230° (c) 130° (d) 50°
  11. 11.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 145° (d) 290°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 90° (c) 135° (d) 46°
  13. 13.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 230° (b) 100° (c) 130° (d) 50°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 160° (c) 20° (d) 10°
  15. 15.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 145° (b) 105° (c) 70° (d) 110°
  16. 16.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 135° (b) 225° (c) 90° (d) 45°
  17. 17.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 75° (c) 105° (d) 160°
  18. 18.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 85° (b) 110° (c) 95° (d) 155°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 81° (c) 100° (d) 160°
  20. 20.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 20° (c) 110° (d) 70°
  21. 21.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 110° (d) 130°
  22. 22.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 115° (b) 100° (c) 65° (d) 145°
  23. 23.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 150° (c) 30° (d) 60°
  24. 24.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 60° (b) 25° (c) 145° (d) 155°
  25. 25.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 40° (b) 120° (c) 140° (d) 100°
  26. 26.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 95° (b) 160° (c) 105° (d) 85°
  27. 27.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 125° (d) 70°
  28. 28.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 150° (b) 95° (c) 85° (d) 125°
  29. 29.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 215° (c) 70° (d) 35°
  30. 30.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 255° (b) 150° (c) 105° (d) 75°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 10°
  32. 32.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 140° (b) 60° (c) 160° (d) 20°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 15° (c) 16° (d) 165°
  34. 34.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 235° (b) 55° (c) 125° (d) 110°
  35. 35.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 86° (d) 265°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 145° (c) 35° (d) 36°
  37. 37.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 115° (c) 80° (d) 100°
  38. 38.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 40° (c) 140° (d) 100°
  39. 39.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°
  40. 40.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 165° (b) 115° (c) 80° (d) 15°

Answer key

  1. 120°
  2. 135°
  3. 90°
  4. 35°
  5. 90°
  6. 50°
  7. 115°
  8. 60°
  9. 135°
  10. 50°
  11. 70°
  12. 45°
  13. 50°
  14. 10°
  15. 70°
  16. 45°
  17. 75°
  18. 95°
  19. 80°
  20. 40°
  21. 120°
  22. 65°
  23. 120°
  24. 25°
  25. 140°
  26. 85°
  27. 70°
  28. 95°
  29. 35°
  30. 105°
  31. 50°
  32. 20°
  33. 15°
  34. 125°
  35. 85°
  36. 35°
  37. 100°
  38. 100°
  39. 80°
  40. 15°

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