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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 590 · 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 20° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 140° (c) 60° (d) 160°
  2. 2.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 160° (b) 55° (c) 145° (d) 35°
  3. 3.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 5° (d) 275°
  4. 4.Two angles of a triangle are 25° and 145°. What is the third angle? (a) 10° (b) 170° (c) 35° (d) 155°
  5. 5.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 125° (b) 30° (c) 85° (d) 150°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 10° (b) 85° (c) 95° (d) 190°
  7. 7.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 105° (b) 285° (c) 75° (d) 15°
  8. 8.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 125° (b) 105° (c) 55° (d) 130°
  9. 9.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 160° (b) 70° (c) 110° (d) 130°
  10. 10.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 145° (b) 70° (c) 290° (d) 110°
  11. 11.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) 130° (c) 310° (d) 50°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 300° (c) 30° (d) 150°
  13. 13.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 75° (b) 30° (c) 135° (d) 150°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 36° (c) 35° (d) 145°
  15. 15.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 85° (d) 130°
  16. 16.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 160° (b) 70° (c) 130° (d) 110°
  17. 17.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 115° (b) 105° (c) 40° (d) 140°
  18. 18.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 75° (c) 160° (d) 105°
  19. 19.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 60° (c) 300° (d) 120°
  20. 20.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 46° (b) 45° (c) 225° (d) 135°
  21. 21.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 160° (c) 20° (d) 140°
  22. 22.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 50° (b) 90° (c) 140° (d) 130°
  23. 23.Two angles of a triangle are 45° and 100°. What is the third angle? (a) 80° (b) 145° (c) 35° (d) 135°
  24. 24.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
  25. 25.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 15° (d) 30°
  26. 26.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 70° (c) 20° (d) 110°
  27. 27.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 80° (c) 10° (d) 100°
  28. 28.Two angles of a triangle are 80° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 145° (d) 35°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 90° (d) 45°
  30. 30.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 125° (b) 70° (c) 250° (d) 55°
  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) 61° (c) 60° (d) 120°
  32. 32.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 110° (b) 165° (c) 85° (d) 15°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 160° (c) 81° (d) 80°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 11° (c) 10° (d) 160°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 25° (d) 50°
  36. 36.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 140° (d) 155°
  37. 37.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 75° (b) 105° (c) 135° (d) 150°
  38. 38.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 55° (c) 35° (d) 145°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 55° (c) 20° (d) 110°
  40. 40.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 150° (b) 55° (c) 85° (d) 125°

Answer key

  1. 60°
  2. 145°
  3. 95°
  4. 10°
  5. 150°
  6. 95°
  7. 105°
  8. 55°
  9. 110°
  10. 110°
  11. 130°
  12. 150°
  13. 30°
  14. 35°
  15. 85°
  16. 110°
  17. 40°
  18. 105°
  19. 120°
  20. 45°
  21. 160°
  22. 130°
  23. 35°
  24. 60°
  25. 30°
  26. 40°
  27. 100°
  28. 145°
  29. 45°
  30. 125°
  31. 60°
  32. 15°
  33. 80°
  34. 10°
  35. 25°
  36. 65°
  37. 105°
  38. 110°
  39. 55°
  40. 55°

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