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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 15 · 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 110°. What is the third angle? (a) 40° (b) 70° (c) 150° (d) 140°
  2. 2.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 145° (d) 80°
  3. 3.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 35° (b) 105° (c) 110° (d) 145°
  4. 4.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 55° (b) 160° (c) 145° (d) 125°
  5. 5.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 130° (c) 25° (d) 65°
  6. 6.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 160° (c) 100° (d) 260°
  7. 7.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 55° (b) 105° (c) 130° (d) 125°
  8. 8.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 20° (c) 110° (d) 70°
  9. 9.Two angles of a triangle are 40° and 75°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 65°
  10. 10.Two angles of a triangle are 60° and 45°. What is the third angle? (a) 135° (b) 120° (c) 75° (d) 105°
  11. 11.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 140° (d) 120°
  12. 12.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 45° (c) 135° (d) 91°
  13. 13.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 50° (c) 40° (d) 130°
  14. 14.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) 41° (d) 40°
  15. 15.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 40° (d) 100°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 75° (b) 30° (c) 210° (d) 105°
  17. 17.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 50° (b) 95° (c) 135° (d) 130°
  18. 18.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 50° (c) 40° (d) 140°
  19. 19.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 30° (b) 210° (c) 150° (d) 105°
  20. 20.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 70° (c) 340° (d) 160°
  21. 21.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 150° (c) 115° (d) 30°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 70° (c) 40° (d) 50°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 86° (c) 85° (d) 95°
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 20° (c) 100° (d) 200°
  25. 25.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 80° (c) 100° (d) 10°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 80° (c) 50° (d) 100°
  27. 27.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 170° (b) 150° (c) 40° (d) 10°
  28. 28.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 135° (b) 70° (c) 155° (d) 45°
  29. 29.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 35° (b) 100° (c) 145° (d) 115°
  30. 30.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 20° (b) 160° (c) 90° (d) 110°
  31. 31.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°
  32. 32.Two angles of a triangle are 20° and 20°. What is the exterior angle at the third corner? (a) 140° (b) 40° (c) 160° (d) 320°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 115° (c) 66° (d) 130°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 130° (c) 40° (d) 50°
  35. 35.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 135° (b) 85° (c) 130° (d) 95°
  36. 36.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 250° (d) 140°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 40° (c) 60° (d) 120°
  38. 38.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 85° (b) 125° (c) 95° (d) 140°
  39. 39.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 160° (b) 85° (c) 65° (d) 115°
  40. 40.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 160° (b) 10° (c) 30° (d) 170°

Answer key

  1. 40°
  2. 100°
  3. 145°
  4. 55°
  5. 130°
  6. 100°
  7. 55°
  8. 40°
  9. 65°
  10. 75°
  11. 100°
  12. 90°
  13. 80°
  14. 40°
  15. 100°
  16. 105°
  17. 50°
  18. 140°
  19. 150°
  20. 160°
  21. 150°
  22. 70°
  23. 85°
  24. 100°
  25. 20°
  26. 50°
  27. 10°
  28. 135°
  29. 145°
  30. 20°
  31. 85°
  32. 40°
  33. 65°
  34. 65°
  35. 85°
  36. 110°
  37. 30°
  38. 95°
  39. 115°
  40. 10°

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