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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 607 · 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.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) 20° (d) 140°
  2. 2.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 75° (c) 145° (d) 105°
  3. 3.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 55° (b) 145° (c) 125° (d) 160°
  4. 4.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 70° (b) 160° (c) 90° (d) 110°
  5. 5.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 120° (b) 90° (c) 60° (d) 150°
  6. 6.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 140° (b) 40° (c) 41° (d) 220°
  7. 7.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 55° (b) 160° (c) 125° (d) 145°
  8. 8.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 340° (c) 70° (d) 160°
  9. 9.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 140° (b) 80° (c) 120° (d) 100°
  10. 10.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 100° (c) 140° (d) 50°
  11. 11.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 230° (b) 130° (c) 50° (d) 115°
  12. 12.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 65° (b) 130° (c) 115° (d) 245°
  13. 13.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 25° (c) 50° (d) 130°
  14. 14.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 120° (d) 150°
  15. 15.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 60° (b) 140° (c) 20° (d) 160°
  16. 16.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 170° (b) 10° (c) 135° (d) 55°
  17. 17.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 140° (b) 250° (c) 70° (d) 110°
  18. 18.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 100° (c) 20° (d) 10°
  19. 19.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) 85° (d) 86°
  20. 20.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 20° (b) 115° (c) 160° (d) 85°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 20° (c) 160° (d) 40°
  22. 22.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 45° (b) 90° (c) 135° (d) 225°
  23. 23.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 120° (b) 85° (c) 155° (d) 60°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 70° (c) 145° (d) 36°
  25. 25.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 220° (c) 40° (d) 110°
  26. 26.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 45° (c) 100° (d) 135°
  27. 27.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 85° (c) 95° (d) 160°
  28. 28.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 160° (b) 200° (c) 20° (d) 100°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 130° (c) 115° (d) 66°
  30. 30.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 215° (c) 36° (d) 35°
  31. 31.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 86° (d) 265°
  32. 32.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 26° (c) 155° (d) 25°
  33. 33.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) 115° (c) 245° (d) 65°
  34. 34.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 155° (b) 125° (c) 150° (d) 55°
  35. 35.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 70° (b) 290° (c) 110° (d) 145°
  36. 36.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 225° (b) 135° (c) 45° (d) 46°
  37. 37.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 80° (b) 115° (c) 15° (d) 165°
  38. 38.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
  39. 39.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 70° (b) 90° (c) 160° (d) 110°
  40. 40.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°

Answer key

  1. 20°
  2. 105°
  3. 125°
  4. 110°
  5. 60°
  6. 40°
  7. 125°
  8. 160°
  9. 80°
  10. 100°
  11. 130°
  12. 115°
  13. 25°
  14. 120°
  15. 20°
  16. 10°
  17. 70°
  18. 20°
  19. 85°
  20. 20°
  21. 20°
  22. 135°
  23. 60°
  24. 35°
  25. 110°
  26. 135°
  27. 85°
  28. 20°
  29. 65°
  30. 35°
  31. 85°
  32. 25°
  33. 65°
  34. 125°
  35. 110°
  36. 45°
  37. 15°
  38. 10°
  39. 70°
  40. 120°

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