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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 364 · 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 65°. What is the third angle? (a) 55° (b) 115° (c) 120° (d) 125°
  2. 2.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 130° (c) 65° (d) 155°
  3. 3.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 80° (b) 140° (c) 100° (d) 280°
  4. 4.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 140° (c) 40° (d) 320°
  5. 5.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 85° (b) 150° (c) 95° (d) 115°
  6. 6.Two angles of a triangle are 55° and 85°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 125° (d) 95°
  7. 7.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 45° (c) 90° (d) 135°
  8. 8.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 60° (b) 140° (c) 160° (d) 120°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 20° (c) 40° (d) 140°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 80° (c) 50° (d) 10°
  11. 11.Two angles of a triangle are 30° and 135°. What is the third angle? (a) 45° (b) 150° (c) 15° (d) 165°
  12. 12.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 60° (c) 160° (d) 120°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 85° (c) 86° (d) 95°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 75° (c) 30° (d) 60°
  15. 15.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 100° (c) 10° (d) 20°
  16. 16.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 160° (b) 140° (c) 120° (d) 60°
  17. 17.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 120° (b) 240° (c) 61° (d) 60°
  18. 18.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 10° (c) 85° (d) 5°
  19. 19.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 55° (b) 110° (c) 125° (d) 235°
  20. 20.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 100° (c) 50° (d) 140°
  21. 21.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 110° (b) 105° (c) 70° (d) 145°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 11° (d) 10°
  23. 23.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 55° (c) 35° (d) 125°
  24. 24.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 55° (c) 35° (d) 125°
  25. 25.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 60° (c) 150° (d) 120°
  26. 26.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 155° (b) 25° (c) 100° (d) 105°
  27. 27.Two angles of a triangle are 50° and 45°. What is the exterior angle at the third corner? (a) 85° (b) 135° (c) 95° (d) 130°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 80° (c) 20° (d) 100°
  29. 29.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 110° (c) 20° (d) 70°
  30. 30.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 90° (b) 270° (c) 120° (d) 150°
  31. 31.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 150° (d) 160°
  32. 32.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 65° (b) 245° (c) 115° (d) 66°
  33. 33.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 160° (c) 95° (d) 85°
  34. 34.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 125° (b) 115° (c) 60° (d) 120°
  35. 35.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 95° (b) 135° (c) 85° (d) 130°
  36. 36.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 45° (b) 80° (c) 145° (d) 135°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 40° (c) 130° (d) 65°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 125° (d) 55°
  39. 39.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 95° (b) 160° (c) 85° (d) 105°
  40. 40.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 105° (d) 30°

Answer key

  1. 55°
  2. 130°
  3. 100°
  4. 140°
  5. 95°
  6. 140°
  7. 90°
  8. 120°
  9. 20°
  10. 50°
  11. 15°
  12. 120°
  13. 85°
  14. 75°
  15. 20°
  16. 60°
  17. 60°
  18. 10°
  19. 125°
  20. 100°
  21. 70°
  22. 10°
  23. 70°
  24. 125°
  25. 120°
  26. 25°
  27. 95°
  28. 100°
  29. 40°
  30. 90°
  31. 50°
  32. 65°
  33. 85°
  34. 60°
  35. 85°
  36. 135°
  37. 65°
  38. 125°
  39. 85°
  40. 30°

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