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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 566 · 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 120°. What is the third angle? (a) 40° (b) 160° (c) 140° (d) 60°
  2. 2.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 155° (c) 60° (d) 120°
  3. 3.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 150° (b) 80° (c) 130° (d) 50°
  4. 4.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 135° (b) 145° (c) 100° (d) 80°
  5. 5.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 25° (b) 100° (c) 155° (d) 105°
  6. 6.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 75° (b) 145° (c) 105° (d) 140°
  7. 7.Two angles of a triangle are 55° and 55°. What is the exterior angle at the third corner? (a) 250° (b) 125° (c) 70° (d) 110°
  8. 8.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 85° (c) 5° (d) 95°
  9. 9.Two angles of a triangle are 40° and 110°. What is the exterior angle at the third corner? (a) 70° (b) 30° (c) 140° (d) 150°
  10. 10.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°
  11. 11.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 110° (d) 50°
  12. 12.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 25° (c) 130° (d) 155°
  13. 13.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 65° (b) 155° (c) 115° (d) 140°
  14. 14.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 85° (b) 125° (c) 140° (d) 95°
  15. 15.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 75° (d) 145°
  16. 16.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 145° (b) 110° (c) 75° (d) 105°
  17. 17.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 140° (b) 40° (c) 80° (d) 220°
  18. 18.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 45° (c) 110° (d) 35°
  19. 19.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 155° (b) 80° (c) 25° (d) 125°
  20. 20.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 295° (c) 65° (d) 115°
  21. 21.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 130° (b) 125° (c) 105° (d) 50°
  22. 22.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) 240° (c) 120° (d) 60°
  23. 23.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 80° (c) 100° (d) 280°
  24. 24.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 125° (d) 145°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 70° (c) 110° (d) 55°
  26. 26.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 115° (b) 150° (c) 95° (d) 85°
  27. 27.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 130° (c) 50° (d) 80°
  28. 28.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 55° (b) 35° (c) 125° (d) 305°
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 60° (b) 61° (c) 59° (d) 120°
  30. 30.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 60° (b) 150° (c) 300° (d) 120°
  31. 31.Two angles of a triangle are 65° and 95°. What is the third angle? (a) 85° (b) 115° (c) 160° (d) 20°
  32. 32.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 105° (c) 15° (d) 75°
  33. 33.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) 10° (c) 100° (d) 80°
  34. 34.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 100° (b) 150° (c) 70° (d) 110°
  35. 35.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 105° (c) 145° (d) 70°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 140° (c) 30° (d) 20°
  37. 37.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 35° (d) 70°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 60° (c) 120° (d) 70°
  39. 39.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 90° (c) 135° (d) 45°
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 70° (c) 36° (d) 145°

Answer key

  1. 40°
  2. 60°
  3. 130°
  4. 80°
  5. 25°
  6. 105°
  7. 110°
  8. 95°
  9. 150°
  10. 125°
  11. 130°
  12. 130°
  13. 115°
  14. 95°
  15. 105°
  16. 75°
  17. 40°
  18. 35°
  19. 25°
  20. 115°
  21. 50°
  22. 60°
  23. 80°
  24. 90°
  25. 55°
  26. 85°
  27. 80°
  28. 125°
  29. 60°
  30. 120°
  31. 20°
  32. 30°
  33. 100°
  34. 70°
  35. 110°
  36. 20°
  37. 70°
  38. 60°
  39. 90°
  40. 35°

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