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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 834 · 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 50°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 110° (d) 70°
  2. 2.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 105° (b) 115° (c) 140° (d) 40°
  3. 3.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 190° (b) 11° (c) 10° (d) 170°
  4. 4.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 50° (c) 25° (d) 115°
  5. 5.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 145° (b) 270° (c) 125° (d) 90°
  6. 6.Two angles of a triangle are 55° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 125° (c) 140° (d) 40°
  7. 7.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 75° (b) 150° (c) 105° (d) 135°
  8. 8.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 80° (b) 135° (c) 145° (d) 100°
  9. 9.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 20° (c) 100° (d) 80°
  10. 10.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 150° (b) 60° (c) 90° (d) 120°
  11. 11.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) 86° (d) 85°
  12. 12.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 120° (c) 240° (d) 60°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 55° (c) 56° (d) 125°
  14. 14.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 105° (b) 45° (c) 120° (d) 135°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 90° (b) 135° (c) 46° (d) 45°
  16. 16.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 110° (b) 55° (c) 125° (d) 235°
  17. 17.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 50° (c) 40° (d) 130°
  18. 18.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 60° (b) 125° (c) 115° (d) 120°
  19. 19.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 55° (b) 35° (c) 325° (d) 145°
  20. 20.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 125° (b) 160° (c) 105° (d) 75°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 80° (d) 20°
  22. 22.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 10° (b) 150° (c) 40° (d) 170°
  23. 23.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 155° (b) 55° (c) 150° (d) 125°
  24. 24.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 25° (d) 130°
  25. 25.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 55° (b) 145° (c) 160° (d) 125°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 100° (b) 40° (c) 50° (d) 80°
  27. 27.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 120° (d) 30°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 90° (c) 45° (d) 135°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 25° (c) 155° (d) 130°
  30. 30.Two angles of a triangle are 55° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 235° (c) 55° (d) 125°
  31. 31.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 35° (c) 55° (d) 145°
  32. 32.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 110° (b) 105° (c) 70° (d) 145°
  33. 33.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 155° (b) 135° (c) 70° (d) 45°
  34. 34.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 25° (c) 65° (d) 155°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 81° (c) 80° (d) 100°
  36. 36.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°
  37. 37.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 330° (d) 150°
  38. 38.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 80° (b) 110° (c) 10° (d) 170°
  39. 39.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 60° (b) 115° (c) 120° (d) 125°
  40. 40.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 51° (c) 130° (d) 50°

Answer key

  1. 110°
  2. 140°
  3. 10°
  4. 50°
  5. 90°
  6. 140°
  7. 105°
  8. 100°
  9. 20°
  10. 60°
  11. 85°
  12. 60°
  13. 55°
  14. 45°
  15. 45°
  16. 55°
  17. 130°
  18. 120°
  19. 145°
  20. 105°
  21. 80°
  22. 10°
  23. 125°
  24. 130°
  25. 55°
  26. 40°
  27. 120°
  28. 135°
  29. 155°
  30. 125°
  31. 110°
  32. 70°
  33. 45°
  34. 155°
  35. 80°
  36. 160°
  37. 150°
  38. 10°
  39. 120°
  40. 50°

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