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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 513 · 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 60° and 55°. What is the third angle? (a) 115° (b) 120° (c) 65° (d) 125°
  2. 2.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 100° (c) 50° (d) 140°
  3. 3.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 85° (c) 95° (d) 10°
  4. 4.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 140° (b) 40° (c) 160° (d) 60°
  5. 5.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 300° (c) 120° (d) 60°
  6. 6.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°
  7. 7.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 40° (b) 200° (c) 160° (d) 20°
  8. 8.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 10° (c) 280° (d) 100°
  9. 9.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 130° (b) 155° (c) 310° (d) 50°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 170° (c) 86° (d) 85°
  11. 11.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 110° (d) 130°
  12. 12.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 120° (b) 90° (c) 30° (d) 150°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 50° (b) 155° (c) 25° (d) 26°
  14. 14.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 145° (c) 120° (d) 95°
  15. 15.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 85° (b) 110° (c) 95° (d) 155°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 80° (c) 50° (d) 100°
  17. 17.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 30° (b) 115° (c) 150° (d) 95°
  18. 18.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 110° (b) 70° (c) 120° (d) 130°
  19. 19.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 110° (b) 135° (c) 65° (d) 115°
  20. 20.Two angles of a triangle are 60° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 50° (c) 120° (d) 130°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 240° (c) 60° (d) 120°
  22. 22.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 20° (b) 21° (c) 40° (d) 160°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 45° (c) 90° (d) 135°
  24. 24.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 140° (b) 85° (c) 40° (d) 135°
  25. 25.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 45° (d) 90°
  26. 26.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 55° (b) 160° (c) 145° (d) 125°
  27. 27.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 50° (d) 25°
  28. 28.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) 200° (d) 20°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 20° (c) 160° (d) 320°
  30. 30.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 10° (c) 190° (d) 170°
  31. 31.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 125° (b) 130° (c) 50° (d) 105°
  32. 32.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 115° (b) 165° (c) 80° (d) 15°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 60° (d) 30°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 40° (c) 140° (d) 20°
  35. 35.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 105° (c) 76° (d) 75°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 80° (c) 81° (d) 100°
  37. 37.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 160° (c) 105° (d) 75°
  38. 38.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) 205° (c) 26° (d) 25°
  39. 39.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 130° (c) 55° (d) 125°
  40. 40.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 325° (c) 55° (d) 145°

Answer key

  1. 65°
  2. 100°
  3. 10°
  4. 40°
  5. 120°
  6. 75°
  7. 20°
  8. 100°
  9. 130°
  10. 85°
  11. 120°
  12. 30°
  13. 25°
  14. 95°
  15. 85°
  16. 50°
  17. 150°
  18. 70°
  19. 65°
  20. 130°
  21. 120°
  22. 20°
  23. 135°
  24. 140°
  25. 90°
  26. 125°
  27. 50°
  28. 20°
  29. 160°
  30. 10°
  31. 50°
  32. 15°
  33. 60°
  34. 20°
  35. 75°
  36. 80°
  37. 105°
  38. 25°
  39. 125°
  40. 145°

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