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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 243 · 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 30° and 40°. What is the third angle? (a) 140° (b) 150° (c) 110° (d) 70°
  2. 2.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 55° (b) 145° (c) 160° (d) 20°
  3. 3.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 100° (d) 105°
  4. 4.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 120° (c) 30° (d) 61°
  5. 5.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 140° (b) 105° (c) 75° (d) 145°
  6. 6.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 56° (c) 235° (d) 55°
  7. 7.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 135° (b) 95° (c) 130° (d) 85°
  8. 8.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 45° (b) 135° (c) 115° (d) 110°
  9. 9.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 65° (d) 130°
  10. 10.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 65° (b) 145° (c) 150° (d) 115°
  11. 11.Two angles of a triangle are 30° and 95°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 150° (d) 85°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 120° (c) 60° (d) 40°
  13. 13.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 55° (c) 305° (d) 125°
  14. 14.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 105° (b) 150° (c) 75° (d) 135°
  15. 15.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 110° (c) 70° (d) 55°
  16. 16.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 105° (d) 110°
  17. 17.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 115° (b) 55° (c) 125° (d) 120°
  18. 18.Two angles of a triangle are 60° and 110°. What is the third angle? (a) 170° (b) 120° (c) 10° (d) 70°
  19. 19.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 215° (b) 70° (c) 145° (d) 35°
  20. 20.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 95° (b) 45° (c) 130° (d) 135°
  21. 21.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 160° (c) 70° (d) 20°
  22. 22.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 35° (d) 145°
  23. 23.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 110° (b) 35° (c) 105° (d) 145°
  24. 24.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 70° (b) 110° (c) 145° (d) 105°
  25. 25.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 40° (d) 140°
  26. 26.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 135° (b) 85° (c) 140° (d) 95°
  27. 27.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 120° (b) 115° (c) 60° (d) 125°
  28. 28.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 130° (b) 65° (c) 115° (d) 245°
  29. 29.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 55° (c) 110° (d) 35°
  30. 30.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 75° (d) 150°
  31. 31.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 60° (b) 120° (c) 140° (d) 100°
  32. 32.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 80° (c) 160° (d) 20°
  33. 33.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 70° (b) 110° (c) 150° (d) 100°
  34. 34.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 325° (c) 55° (d) 35°
  35. 35.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 135° (d) 155°
  36. 36.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 65° (b) 245° (c) 115° (d) 66°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 61° (c) 120° (d) 60°
  38. 38.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 65° (c) 25° (d) 115°
  39. 39.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 145° (b) 100° (c) 65° (d) 115°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 120° (b) 240° (c) 121° (d) 60°

Answer key

  1. 110°
  2. 20°
  3. 100°
  4. 60°
  5. 105°
  6. 55°
  7. 85°
  8. 45°
  9. 130°
  10. 65°
  11. 125°
  12. 30°
  13. 125°
  14. 75°
  15. 55°
  16. 145°
  17. 55°
  18. 10°
  19. 145°
  20. 45°
  21. 160°
  22. 145°
  23. 35°
  24. 70°
  25. 140°
  26. 95°
  27. 60°
  28. 65°
  29. 110°
  30. 135°
  31. 60°
  32. 80°
  33. 70°
  34. 145°
  35. 70°
  36. 65°
  37. 60°
  38. 115°
  39. 65°
  40. 120°

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