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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 617 · 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 95°. What is the exterior angle at the third corner? (a) 85° (b) 145° (c) 130° (d) 50°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 40° (c) 280° (d) 140°
  3. 3.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 55° (c) 110° (d) 35°
  4. 4.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°
  5. 5.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 55° (b) 125° (c) 145° (d) 90°
  6. 6.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 115° (b) 75° (c) 170° (d) 10°
  7. 7.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 80° (b) 115° (c) 145° (d) 100°
  8. 8.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 125° (b) 150° (c) 155° (d) 55°
  9. 9.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 125° (d) 70°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 80° (d) 70°
  11. 11.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 20° (c) 70° (d) 160°
  12. 12.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 110° (b) 155° (c) 85° (d) 95°
  13. 13.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 100° (d) 115°
  14. 14.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 15° (c) 165° (d) 195°
  15. 15.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 120° (b) 300° (c) 30° (d) 60°
  16. 16.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 130° (b) 70° (c) 120° (d) 110°
  17. 17.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 30° (d) 120°
  18. 18.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 65°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 15° (c) 150° (d) 25°
  20. 20.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 110° (d) 145°
  21. 21.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 140° (d) 120°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 140° (c) 50° (d) 40°
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 85° (c) 10° (d) 95°
  24. 24.Two angles of a triangle are 60° and 110°. What is the third angle? (a) 70° (b) 120° (c) 10° (d) 170°
  25. 25.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 5° (d) 10°
  26. 26.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 45° (c) 70° (d) 35°
  27. 27.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 140° (d) 40°
  28. 28.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 85° (b) 145° (c) 95° (d) 120°
  29. 29.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 120° (b) 20° (c) 80° (d) 160°
  30. 30.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 30° (d) 150°
  31. 31.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 125° (c) 155° (d) 80°
  32. 32.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 145° (b) 105° (c) 110° (d) 35°
  33. 33.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 140° (b) 125° (c) 85° (d) 95°
  34. 34.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 155° (b) 26° (c) 205° (d) 25°
  35. 35.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 80° (b) 140° (c) 100° (d) 280°
  36. 36.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 50° (c) 80° (d) 10°
  37. 37.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 40° (b) 115° (c) 105° (d) 140°
  38. 38.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) 70° (c) 110° (d) 71°
  39. 39.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 90° (b) 140° (c) 40° (d) 130°
  40. 40.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 30° (b) 170° (c) 10° (d) 160°

Answer key

  1. 130°
  2. 140°
  3. 110°
  4. 60°
  5. 55°
  6. 10°
  7. 100°
  8. 55°
  9. 70°
  10. 80°
  11. 160°
  12. 85°
  13. 145°
  14. 15°
  15. 120°
  16. 70°
  17. 60°
  18. 65°
  19. 15°
  20. 105°
  21. 100°
  22. 70°
  23. 95°
  24. 10°
  25. 10°
  26. 35°
  27. 100°
  28. 95°
  29. 20°
  30. 150°
  31. 80°
  32. 35°
  33. 85°
  34. 25°
  35. 100°
  36. 50°
  37. 40°
  38. 70°
  39. 40°
  40. 10°

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