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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 128 · 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 85°. What is the exterior angle at the third corner? (a) 150° (b) 115° (c) 95° (d) 65°
  2. 2.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 105° (b) 160° (c) 20° (d) 95°
  3. 3.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 165° (b) 105° (c) 90° (d) 15°
  4. 4.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 140° (b) 250° (c) 70° (d) 110°
  5. 5.Two angles of a triangle are 35° and 135°. What is the third angle? (a) 145° (b) 10° (c) 170° (d) 45°
  6. 6.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 135° (c) 160° (d) 115°
  7. 7.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 145° (b) 270° (c) 90° (d) 125°
  8. 8.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 25° (c) 65° (d) 130°
  9. 9.Two angles of a triangle are 30° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 150° (c) 90° (d) 270°
  10. 10.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 145° (d) 75°
  11. 11.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 130° (b) 95° (c) 145° (d) 85°
  12. 12.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 110° (c) 40° (d) 70°
  13. 13.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) 225° (d) 45°
  14. 14.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 265° (c) 86° (d) 95°
  15. 15.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 125° (b) 85° (c) 140° (d) 95°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 40° (c) 60° (d) 30°
  17. 17.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 75° (b) 110° (c) 105° (d) 145°
  18. 18.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°
  19. 19.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 120° (b) 300° (c) 150° (d) 60°
  20. 20.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 45° (d) 135°
  21. 21.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 40° (d) 50°
  22. 22.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 30° (b) 330° (c) 60° (d) 150°
  23. 23.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 65° (b) 125° (c) 120° (d) 115°
  24. 24.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 20° (b) 200° (c) 21° (d) 160°
  25. 25.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 55° (b) 115° (c) 120° (d) 125°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 61° (c) 59° (d) 60°
  27. 27.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 110° (c) 145° (d) 35°
  28. 28.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 140° (b) 115° (c) 40° (d) 105°
  29. 29.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 20° (b) 200° (c) 40° (d) 160°
  30. 30.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 130° (c) 75° (d) 105°
  31. 31.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 245° (b) 65° (c) 130° (d) 115°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 20° (c) 160° (d) 40°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 10° (d) 160°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 150° (c) 25° (d) 15°
  35. 35.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 120° (b) 85° (c) 25° (d) 155°
  36. 36.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 35° (c) 120° (d) 145°
  37. 37.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 45° (b) 140° (c) 135° (d) 85°
  38. 38.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 30° (b) 100° (c) 110° (d) 150°
  39. 39.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 105° (b) 100° (c) 75° (d) 155°
  40. 40.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 165° (b) 55° (c) 140° (d) 15°

Answer key

  1. 115°
  2. 20°
  3. 15°
  4. 70°
  5. 10°
  6. 65°
  7. 90°
  8. 130°
  9. 90°
  10. 105°
  11. 95°
  12. 40°
  13. 45°
  14. 85°
  15. 85°
  16. 30°
  17. 75°
  18. 20°
  19. 60°
  20. 135°
  21. 100°
  22. 150°
  23. 65°
  24. 20°
  25. 125°
  26. 60°
  27. 110°
  28. 140°
  29. 20°
  30. 105°
  31. 115°
  32. 20°
  33. 10°
  34. 15°
  35. 25°
  36. 145°
  37. 45°
  38. 30°
  39. 105°
  40. 15°

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