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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 536 · 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 straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 140° (c) 160° (d) 20°
  2. 2.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) 61° (c) 240° (d) 60°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 125° (c) 70° (d) 250°
  4. 4.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 85° (b) 130° (c) 135° (d) 95°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 100° (c) 20° (d) 80°
  6. 6.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 65° (b) 35° (c) 150° (d) 145°
  7. 7.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 95° (c) 85° (d) 155°
  8. 8.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 75° (b) 105° (c) 145° (d) 140°
  9. 9.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 100° (d) 50°
  10. 10.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) 150° (c) 30° (d) 330°
  11. 11.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 335° (c) 155° (d) 65°
  12. 12.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 80° (b) 125° (c) 135° (d) 100°
  13. 13.Two angles of a triangle are 40° and 45°. What is the third angle? (a) 140° (b) 135° (c) 95° (d) 85°
  14. 14.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 145° (b) 95° (c) 120° (d) 85°
  15. 15.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 160° (b) 130° (c) 110° (d) 70°
  16. 16.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 145° (d) 90°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 260° (c) 80° (d) 130°
  18. 18.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 285° (c) 105° (d) 15°
  19. 19.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 125° (c) 130° (d) 50°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 65° (c) 130° (d) 115°
  21. 21.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 70° (b) 140° (c) 250° (d) 110°
  22. 22.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 15° (b) 115° (c) 80° (d) 165°
  23. 23.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) 325° (c) 35° (d) 145°
  24. 24.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 55° (b) 145° (c) 160° (d) 20°
  25. 25.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 160° (b) 100° (c) 80° (d) 120°
  26. 26.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 95° (c) 85° (d) 145°
  27. 27.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 150° (b) 125° (c) 155° (d) 55°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 30° (b) 31° (c) 60° (d) 150°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 150° (b) 30° (c) 300° (d) 120°
  30. 30.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 105° (b) 135° (c) 120° (d) 60°
  31. 31.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 105° (c) 30° (d) 75°
  32. 32.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 55° (c) 35° (d) 110°
  33. 33.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 125° (c) 55° (d) 70°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 10° (c) 11° (d) 20°
  35. 35.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 225° (c) 45° (d) 46°
  36. 36.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 125° (b) 115° (c) 120° (d) 60°
  37. 37.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 80° (b) 120° (c) 160° (d) 20°
  38. 38.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 155° (b) 105° (c) 75° (d) 130°
  39. 39.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 20° (c) 290° (d) 110°
  40. 40.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) 50° (d) 25°

Answer key

  1. 160°
  2. 60°
  3. 125°
  4. 95°
  5. 100°
  6. 35°
  7. 85°
  8. 105°
  9. 100°
  10. 150°
  11. 155°
  12. 80°
  13. 95°
  14. 85°
  15. 110°
  16. 125°
  17. 130°
  18. 105°
  19. 130°
  20. 65°
  21. 110°
  22. 15°
  23. 145°
  24. 20°
  25. 100°
  26. 95°
  27. 125°
  28. 30°
  29. 150°
  30. 60°
  31. 30°
  32. 110°
  33. 70°
  34. 10°
  35. 45°
  36. 60°
  37. 20°
  38. 75°
  39. 110°
  40. 25°

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