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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 276 · 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 75° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 105° (c) 135° (d) 45°
  2. 2.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 50° (c) 320° (d) 40°
  3. 3.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 20° (c) 80° (d) 100°
  4. 4.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 160° (b) 270° (c) 110° (d) 90°
  5. 5.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 30° (c) 60° (d) 120°
  6. 6.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 100° (b) 140° (c) 120° (d) 80°
  7. 7.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 155° (b) 140° (c) 65° (d) 40°
  8. 8.Two angles of a triangle are 25° and 120°. What is the exterior angle at the third corner? (a) 35° (b) 155° (c) 60° (d) 145°
  9. 9.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 90° (b) 145° (c) 270° (d) 125°
  10. 10.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 70° (d) 125°
  11. 11.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 155° (b) 105° (c) 25° (d) 100°
  12. 12.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 125° (c) 85° (d) 95°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 90° (b) 270° (c) 135° (d) 45°
  14. 14.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 110° (b) 20° (c) 70° (d) 290°
  15. 15.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 270° (b) 135° (c) 90° (d) 91°
  16. 16.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 10° (b) 140° (c) 170° (d) 50°
  17. 17.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 130° (b) 155° (c) 75° (d) 50°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 130° (b) 155° (c) 25° (d) 310°
  19. 19.Two angles of a triangle are 25° and 45°. What is the exterior angle at the third corner? (a) 70° (b) 155° (c) 110° (d) 135°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 140° (c) 40° (d) 50°
  21. 21.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 290° (b) 145° (c) 70° (d) 110°
  22. 22.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 110° (b) 145° (c) 105° (d) 75°
  23. 23.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 125° (b) 235° (c) 55° (d) 110°
  24. 24.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 95° (b) 85° (c) 115° (d) 150°
  25. 25.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 90° (b) 160° (c) 110° (d) 270°
  26. 26.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 170° (b) 10° (c) 160° (d) 30°
  27. 27.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 65° (b) 140° (c) 105° (d) 115°
  28. 28.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 35° (d) 110°
  29. 29.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 145° (b) 115° (c) 100° (d) 65°
  30. 30.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 140° (b) 80° (c) 220° (d) 40°
  31. 31.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 150° (d) 145°
  32. 32.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°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 290° (c) 145° (d) 110°
  34. 34.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 50° (b) 105° (c) 130° (d) 125°
  35. 35.Two angles of a triangle are 40° and 75°. What is the exterior angle at the third corner? (a) 65° (b) 140° (c) 105° (d) 115°
  36. 36.Two angles of a triangle are 55° and 20°. What is the third angle? (a) 75° (b) 125° (c) 105° (d) 160°
  37. 37.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°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 40° (c) 100° (d) 140°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 11° (b) 20° (c) 170° (d) 10°
  40. 40.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 100° (b) 80° (c) 125° (d) 155°

Answer key

  1. 135°
  2. 140°
  3. 20°
  4. 90°
  5. 60°
  6. 80°
  7. 40°
  8. 145°
  9. 90°
  10. 70°
  11. 25°
  12. 85°
  13. 135°
  14. 110°
  15. 90°
  16. 10°
  17. 50°
  18. 155°
  19. 70°
  20. 70°
  21. 70°
  22. 75°
  23. 55°
  24. 85°
  25. 90°
  26. 10°
  27. 65°
  28. 110°
  29. 65°
  30. 140°
  31. 65°
  32. 50°
  33. 145°
  34. 50°
  35. 115°
  36. 105°
  37. 45°
  38. 140°
  39. 10°
  40. 100°

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