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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 409 · 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 35° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 145° (d) 140°
  2. 2.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 50° (b) 230° (c) 130° (d) 115°
  3. 3.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 30° (b) 85° (c) 150° (d) 125°
  4. 4.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 20° (b) 160° (c) 40° (d) 200°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 135° (b) 45° (c) 90° (d) 270°
  6. 6.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 40° (d) 120°
  7. 7.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 25° (b) 26° (c) 155° (d) 205°
  8. 8.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 120° (c) 60° (d) 30°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 100° (d) 40°
  10. 10.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 140° (b) 160° (c) 60° (d) 120°
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 100° (b) 51° (c) 130° (d) 50°
  12. 12.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 80° (b) 155° (c) 125° (d) 100°
  13. 13.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 5° (b) 85° (c) 95° (d) 275°
  14. 14.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 55° (b) 160° (c) 35° (d) 145°
  15. 15.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 110° (d) 70°
  16. 16.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 55° (b) 100° (c) 125° (d) 135°
  17. 17.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 65° (b) 245° (c) 130° (d) 115°
  18. 18.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 55° (b) 100° (c) 135° (d) 125°
  19. 19.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 155° (c) 65° (d) 25°
  20. 20.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 145° (c) 135° (d) 35°
  21. 21.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 70° (d) 125°
  22. 22.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 150° (b) 115° (c) 85° (d) 95°
  23. 23.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 65° (c) 50° (d) 115°
  24. 24.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°
  25. 25.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 110° (b) 95° (c) 85° (d) 155°
  26. 26.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 220° (b) 40° (c) 80° (d) 140°
  27. 27.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 165° (c) 195° (d) 16°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 86° (c) 95° (d) 85°
  29. 29.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 210° (b) 30° (c) 150° (d) 105°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 140° (c) 70° (d) 40°
  31. 31.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 60° (c) 61° (d) 120°
  32. 32.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 145° (d) 110°
  33. 33.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 120° (b) 100° (c) 140° (d) 40°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 60° (b) 150° (c) 30° (d) 31°
  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) 75° (c) 105° (d) 76°
  36. 36.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 150° (b) 105° (c) 255° (d) 75°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 30° (d) 70°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 35° (c) 36° (d) 145°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 105° (c) 30° (d) 210°
  40. 40.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) 280° (c) 10° (d) 100°

Answer key

  1. 75°
  2. 130°
  3. 150°
  4. 20°
  5. 135°
  6. 140°
  7. 25°
  8. 120°
  9. 40°
  10. 120°
  11. 50°
  12. 100°
  13. 95°
  14. 35°
  15. 40°
  16. 55°
  17. 65°
  18. 125°
  19. 130°
  20. 145°
  21. 70°
  22. 85°
  23. 50°
  24. 45°
  25. 95°
  26. 140°
  27. 15°
  28. 85°
  29. 30°
  30. 70°
  31. 60°
  32. 110°
  33. 40°
  34. 30°
  35. 75°
  36. 75°
  37. 60°
  38. 35°
  39. 105°
  40. 100°

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