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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 66 · 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 300°. What is each of the other two angles? (a) 31° (b) 150° (c) 60° (d) 30°
  2. 2.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 150° (c) 105° (d) 75°
  3. 3.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 120° (d) 300°
  4. 4.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 75° (c) 15° (d) 30°
  5. 5.Two angles of a triangle are 20° and 100°. What is the third angle? (a) 160° (b) 80° (c) 60° (d) 120°
  6. 6.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 155° (b) 130° (c) 50° (d) 75°
  7. 7.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 110° (c) 55° (d) 35°
  8. 8.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 170° (b) 130° (c) 60° (d) 10°
  9. 9.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) 85° (c) 95° (d) 86°
  10. 10.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 70° (c) 215° (d) 35°
  11. 11.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 90° (b) 150° (c) 60° (d) 120°
  12. 12.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 105° (b) 170° (c) 10° (d) 85°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 20° (b) 320° (c) 160° (d) 140°
  14. 14.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 85° (b) 160° (c) 115° (d) 95°
  15. 15.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 115° (b) 120° (c) 125° (d) 60°
  16. 16.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 80° (c) 140° (d) 100°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 11° (c) 170° (d) 10°
  18. 18.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 20° (c) 40° (d) 110°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 145° (c) 36° (d) 70°
  20. 20.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 105° (b) 135° (c) 120° (d) 60°
  21. 21.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 270° (b) 145° (c) 90° (d) 125°
  22. 22.Two angles of a triangle are 40° and 110°. What is the third angle? (a) 30° (b) 150° (c) 70° (d) 140°
  23. 23.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 91° (c) 135° (d) 90°
  24. 24.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) 15° (d) 25°
  25. 25.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 130° (b) 100° (c) 230° (d) 50°
  26. 26.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 125° (b) 65° (c) 120° (d) 115°
  27. 27.Two angles of a triangle are 20° and 135°. What is the third angle? (a) 155° (b) 45° (c) 25° (d) 160°
  28. 28.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°
  29. 29.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 130° (d) 110°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 86° (c) 170° (d) 85°
  31. 31.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 95° (b) 145° (c) 130° (d) 85°
  32. 32.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 270° (b) 91° (c) 135° (d) 90°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 125° (c) 55° (d) 70°
  34. 34.Two angles of a triangle are 40° and 30°. What is the third angle? (a) 150° (b) 110° (c) 140° (d) 70°
  35. 35.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 235° (b) 110° (c) 125° (d) 55°
  36. 36.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 100° (b) 155° (c) 75° (d) 105°
  37. 37.Two angles of a triangle are 50° and 100°. What is the exterior angle at the third corner? (a) 30° (b) 80° (c) 150° (d) 130°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 55° (c) 45° (d) 46°
  39. 39.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 160° (c) 105° (d) 85°
  40. 40.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 120° (d) 60°

Answer key

  1. 30°
  2. 75°
  3. 120°
  4. 30°
  5. 60°
  6. 130°
  7. 110°
  8. 10°
  9. 85°
  10. 35°
  11. 60°
  12. 10°
  13. 160°
  14. 95°
  15. 60°
  16. 100°
  17. 10°
  18. 40°
  19. 35°
  20. 60°
  21. 90°
  22. 30°
  23. 90°
  24. 15°
  25. 50°
  26. 65°
  27. 25°
  28. 105°
  29. 120°
  30. 85°
  31. 95°
  32. 90°
  33. 125°
  34. 110°
  35. 125°
  36. 75°
  37. 150°
  38. 45°
  39. 95°
  40. 120°

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