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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 29 · 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 70° and 90°. What is the third angle? (a) 90° (b) 20° (c) 110° (d) 160°
  2. 2.Two angles of a triangle are 70° and 45°. What is the third angle? (a) 115° (b) 110° (c) 65° (d) 135°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 100° (d) 50°
  4. 4.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 20° (d) 80°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 15° (c) 25° (d) 30°
  6. 6.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 65° (b) 130° (c) 245° (d) 115°
  7. 7.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 170° (b) 130° (c) 60° (d) 10°
  8. 8.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°
  9. 9.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 5° (c) 95° (d) 85°
  10. 10.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 135° (d) 110°
  11. 11.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 60° (c) 100° (d) 120°
  12. 12.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 140° (d) 160°
  13. 13.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°
  14. 14.Two angles of a triangle are 35° and 95°. What is the third angle? (a) 130° (b) 145° (c) 50° (d) 85°
  15. 15.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 100° (b) 230° (c) 130° (d) 50°
  16. 16.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 65°
  17. 17.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 290° (b) 70° (c) 110° (d) 145°
  18. 18.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 130° (d) 155°
  19. 19.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 125° (b) 155° (c) 80° (d) 100°
  20. 20.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 150° (b) 70° (c) 140° (d) 110°
  21. 21.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 95° (b) 150° (c) 65° (d) 115°
  22. 22.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 130° (b) 80° (c) 150° (d) 50°
  23. 23.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 160° (b) 135° (c) 115° (d) 65°
  24. 24.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 86° (d) 85°
  25. 25.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 135° (b) 120° (c) 75° (d) 105°
  26. 26.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 115° (b) 170° (c) 75° (d) 10°
  27. 27.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 110° (b) 250° (c) 70° (d) 140°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 150° (d) 300°
  29. 29.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 135° (b) 95° (c) 130° (d) 85°
  30. 30.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 150° (b) 75° (c) 105° (d) 255°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 50° (c) 70° (d) 140°
  32. 32.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 61° (c) 120° (d) 30°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 70° (b) 125° (c) 250° (d) 55°
  34. 34.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 15° (d) 30°
  35. 35.Two angles of a triangle are 55° and 105°. What is the third angle? (a) 160° (b) 20° (c) 125° (d) 75°
  36. 36.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 115° (c) 65° (d) 125°
  37. 37.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 35° (b) 55° (c) 145° (d) 160°
  38. 38.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 50° (d) 135°
  39. 39.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 60° (b) 40° (c) 30° (d) 120°
  40. 40.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 155° (b) 150° (c) 125° (d) 55°

Answer key

  1. 20°
  2. 65°
  3. 40°
  4. 20°
  5. 15°
  6. 115°
  7. 10°
  8. 20°
  9. 10°
  10. 115°
  11. 120°
  12. 60°
  13. 145°
  14. 50°
  15. 130°
  16. 130°
  17. 110°
  18. 75°
  19. 100°
  20. 110°
  21. 65°
  22. 130°
  23. 65°
  24. 85°
  25. 75°
  26. 10°
  27. 70°
  28. 150°
  29. 95°
  30. 75°
  31. 70°
  32. 60°
  33. 125°
  34. 30°
  35. 20°
  36. 115°
  37. 35°
  38. 130°
  39. 30°
  40. 55°

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