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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 394 · 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 35° and 80°. What is the third angle? (a) 145° (b) 100° (c) 65° (d) 115°
  2. 2.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 70° (b) 100° (c) 150° (d) 110°
  3. 3.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 65° (b) 115° (c) 155° (d) 140°
  4. 4.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 140° (d) 70°
  5. 5.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 95° (b) 155° (c) 110° (d) 25°
  6. 6.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 40° (d) 100°
  7. 7.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 140° (d) 40°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 50° (c) 40° (d) 130°
  9. 9.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 160° (c) 150° (d) 50°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 20° (c) 11° (d) 170°
  11. 11.Two angles of a triangle are 45° and 25°. What is the third angle? (a) 135° (b) 155° (c) 70° (d) 110°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 60° (c) 120° (d) 30°
  13. 13.Two angles of a triangle are 65° and 20°. What is the third angle? (a) 115° (b) 85° (c) 95° (d) 160°
  14. 14.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 40° (b) 70° (c) 150° (d) 140°
  15. 15.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 65° (b) 120° (c) 125° (d) 115°
  16. 16.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 30° (b) 105° (c) 150° (d) 210°
  17. 17.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 50° (c) 135° (d) 130°
  18. 18.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 71° (c) 110° (d) 70°
  19. 19.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 80° (b) 280° (c) 140° (d) 100°
  20. 20.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 160° (d) 85°
  21. 21.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 110° (d) 30°
  22. 22.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 5° (b) 95° (c) 275° (d) 85°
  23. 23.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 125° (b) 305° (c) 35° (d) 55°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 10° (c) 50° (d) 80°
  25. 25.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) 60° (c) 120° (d) 240°
  26. 26.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 150° (b) 75° (c) 255° (d) 105°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 170° (c) 86° (d) 85°
  28. 28.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 155° (b) 90° (c) 115° (d) 25°
  29. 29.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 150° (b) 95° (c) 85° (d) 115°
  30. 30.Two angles of a triangle are 55° and 95°. What is the third angle? (a) 150° (b) 125° (c) 85° (d) 30°
  31. 31.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 55° (c) 110° (d) 70°
  32. 32.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 115° (d) 50°
  33. 33.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 5° (d) 10°
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 80° (c) 40° (d) 41°
  35. 35.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) 320° (c) 40° (d) 50°
  36. 36.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 65° (d) 130°
  37. 37.Two angles of a triangle are 20° and 120°. What is the exterior angle at the third corner? (a) 140° (b) 60° (c) 40° (d) 160°
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 140° (d) 280°
  39. 39.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 70° (b) 110° (c) 160° (d) 130°
  40. 40.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 35° (c) 110° (d) 45°

Answer key

  1. 65°
  2. 110°
  3. 115°
  4. 70°
  5. 25°
  6. 100°
  7. 70°
  8. 65°
  9. 50°
  10. 10°
  11. 110°
  12. 60°
  13. 95°
  14. 140°
  15. 65°
  16. 150°
  17. 130°
  18. 70°
  19. 100°
  20. 85°
  21. 150°
  22. 95°
  23. 125°
  24. 50°
  25. 60°
  26. 75°
  27. 85°
  28. 25°
  29. 85°
  30. 30°
  31. 55°
  32. 50°
  33. 10°
  34. 40°
  35. 140°
  36. 130°
  37. 140°
  38. 140°
  39. 110°
  40. 35°

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