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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 780 · 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 90°. What is each of the other two angles? (a) 46° (b) 55° (c) 45° (d) 90°
  2. 2.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 135° (b) 85° (c) 140° (d) 40°
  3. 3.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 56° (b) 125° (c) 55° (d) 235°
  4. 4.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 30° (c) 70° (d) 120°
  5. 5.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 110° (c) 95° (d) 85°
  6. 6.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 170° (b) 140° (c) 50° (d) 10°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 70° (c) 110° (d) 140°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 55° (d) 70°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 45° (c) 70° (d) 35°
  10. 10.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 135° (b) 130° (c) 95° (d) 85°
  11. 11.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 35° (b) 80° (c) 145° (d) 135°
  12. 12.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 40° (b) 320° (c) 140° (d) 160°
  13. 13.Two angles of a triangle are 40° and 105°. What is the third angle? (a) 140° (b) 35° (c) 75° (d) 145°
  14. 14.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 105° (c) 75° (d) 120°
  15. 15.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 120° (d) 60°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 55° (b) 110° (c) 56° (d) 125°
  17. 17.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 30° (b) 145° (c) 65° (d) 150°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 30° (b) 210° (c) 75° (d) 105°
  19. 19.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°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 120° (c) 30° (d) 60°
  21. 21.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 55° (b) 115° (c) 120° (d) 125°
  22. 22.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 145° (b) 55° (c) 160° (d) 125°
  23. 23.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 55° (b) 235° (c) 125° (d) 110°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 10°
  25. 25.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 75° (c) 105° (d) 160°
  26. 26.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 135° (c) 90° (d) 45°
  27. 27.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 45° (b) 75° (c) 135° (d) 150°
  28. 28.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 105° (b) 165° (c) 15° (d) 90°
  29. 29.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 50°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 150° (b) 120° (c) 30° (d) 300°
  31. 31.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 85° (d) 95°
  32. 32.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 135° (b) 110° (c) 115° (d) 65°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 50° (b) 26° (c) 155° (d) 25°
  34. 34.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 70° (c) 110° (d) 120°
  35. 35.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 50° (c) 65° (d) 115°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 50° (d) 70°
  37. 37.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 120° (b) 80° (c) 100° (d) 140°
  38. 38.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 100° (b) 125° (c) 55° (d) 135°
  39. 39.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 140° (c) 120° (d) 40°
  40. 40.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 145° (b) 65° (c) 115° (d) 100°

Answer key

  1. 45°
  2. 140°
  3. 55°
  4. 60°
  5. 95°
  6. 10°
  7. 70°
  8. 55°
  9. 35°
  10. 85°
  11. 145°
  12. 40°
  13. 35°
  14. 105°
  15. 60°
  16. 55°
  17. 30°
  18. 105°
  19. 130°
  20. 30°
  21. 125°
  22. 125°
  23. 125°
  24. 50°
  25. 105°
  26. 90°
  27. 45°
  28. 15°
  29. 100°
  30. 150°
  31. 95°
  32. 65°
  33. 25°
  34. 110°
  35. 50°
  36. 70°
  37. 80°
  38. 55°
  39. 140°
  40. 115°

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