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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 30 · 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 50°. What is each of the other two angles? (a) 25° (b) 155° (c) 130° (d) 310°
  2. 2.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 80° (b) 150° (c) 110° (d) 100°
  3. 3.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 105° (b) 170° (c) 10° (d) 85°
  4. 4.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 60° (d) 120°
  5. 5.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 145° (b) 100° (c) 115° (d) 80°
  6. 6.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 160° (b) 70° (c) 130° (d) 110°
  7. 7.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 85° (b) 120° (c) 95° (d) 145°
  8. 8.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 130° (c) 105° (d) 75°
  9. 9.Two angles of a triangle are 55° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 40° (c) 140° (d) 125°
  10. 10.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 30° (b) 135° (c) 150° (d) 75°
  11. 11.Two angles of a triangle are 70° and 60°. What is the third angle? (a) 120° (b) 110° (c) 50° (d) 130°
  12. 12.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 145° (b) 160° (c) 35° (d) 55°
  13. 13.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°
  14. 14.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 90° (b) 270° (c) 125° (d) 145°
  15. 15.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 135° (d) 120°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 130° (d) 65°
  17. 17.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 65° (b) 30° (c) 145° (d) 150°
  18. 18.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 85° (c) 15° (d) 110°
  19. 19.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 145° (d) 130°
  20. 20.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 110° (d) 145°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 30° (c) 20° (d) 40°
  22. 22.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 61° (c) 60° (d) 120°
  23. 23.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 245° (c) 65° (d) 115°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 60° (c) 30° (d) 75°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 100° (c) 40° (d) 80°
  26. 26.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 70° (b) 110° (c) 100° (d) 150°
  27. 27.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 85° (c) 5° (d) 95°
  28. 28.Two angles of a triangle are 65° and 40°. What is the third angle? (a) 105° (b) 75° (c) 140° (d) 115°
  29. 29.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 100° (b) 145° (c) 65° (d) 115°
  30. 30.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) 135° (c) 45° (d) 225°
  31. 31.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 45° (b) 110° (c) 135° (d) 115°
  32. 32.Two angles of a triangle are 55° and 95°. What is the third angle? (a) 150° (b) 125° (c) 30° (d) 85°
  33. 33.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 35° (c) 150° (d) 145°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 46° (c) 90° (d) 55°
  35. 35.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 190° (b) 170° (c) 10° (d) 11°
  36. 36.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 265° (c) 95° (d) 85°
  37. 37.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 125° (b) 85° (c) 140° (d) 95°
  38. 38.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°
  39. 39.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 100° (b) 160° (c) 80° (d) 260°
  40. 40.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 95° (b) 40° (c) 140° (d) 125°

Answer key

  1. 155°
  2. 100°
  3. 10°
  4. 120°
  5. 80°
  6. 70°
  7. 85°
  8. 75°
  9. 140°
  10. 30°
  11. 50°
  12. 35°
  13. 140°
  14. 90°
  15. 105°
  16. 65°
  17. 30°
  18. 15°
  19. 85°
  20. 110°
  21. 20°
  22. 60°
  23. 65°
  24. 75°
  25. 40°
  26. 70°
  27. 10°
  28. 75°
  29. 65°
  30. 45°
  31. 135°
  32. 30°
  33. 145°
  34. 45°
  35. 10°
  36. 85°
  37. 85°
  38. 130°
  39. 80°
  40. 40°

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