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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 190 · 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 115°. What is the third angle? (a) 150° (b) 65° (c) 145° (d) 30°
  2. 2.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 125° (b) 115° (c) 65° (d) 120°
  3. 3.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 30° (c) 60° (d) 150°
  4. 4.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 145° (b) 115° (c) 65° (d) 100°
  5. 5.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 145° (c) 130° (d) 85°
  6. 6.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 135° (b) 100° (c) 125° (d) 45°
  7. 7.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 135° (b) 45° (c) 75° (d) 150°
  8. 8.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 60° (b) 30° (c) 120° (d) 300°
  9. 9.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 310° (c) 130° (d) 50°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 95° (c) 170° (d) 85°
  11. 11.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 190° (c) 10° (d) 170°
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 290° (c) 145° (d) 110°
  13. 13.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 250° (b) 125° (c) 70° (d) 110°
  14. 14.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 130° (b) 145° (c) 85° (d) 95°
  15. 15.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 140° (c) 100° (d) 80°
  16. 16.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 85° (c) 160° (d) 95°
  17. 17.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 125° (c) 120° (d) 60°
  18. 18.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 65° (b) 35° (c) 150° (d) 145°
  19. 19.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 90° (b) 30° (c) 150° (d) 120°
  20. 20.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 20° (c) 70° (d) 40°
  21. 21.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 75° (c) 105° (d) 15°
  22. 22.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 95° (b) 115° (c) 30° (d) 150°
  23. 23.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 40° (b) 140° (c) 100° (d) 120°
  24. 24.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 70° (c) 110° (d) 250°
  25. 25.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 16° (c) 195° (d) 15°
  26. 26.Two angles of a triangle are 20° and 105°. What is the exterior angle at the third corner? (a) 160° (b) 55° (c) 75° (d) 125°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 30° (d) 70°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 40° (c) 140° (d) 80°
  29. 29.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 105° (c) 130° (d) 50°
  30. 30.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 150° (b) 115° (c) 85° (d) 95°
  31. 31.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 165° (b) 50° (c) 145° (d) 15°
  32. 32.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 120° (b) 150° (c) 270° (d) 90°
  33. 33.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 100° (b) 110° (c) 80° (d) 150°
  34. 34.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 10° (c) 280° (d) 100°
  35. 35.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 105° (b) 95° (c) 85° (d) 160°
  36. 36.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 135° (b) 100° (c) 45° (d) 125°
  37. 37.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 80° (b) 155° (c) 100° (d) 125°
  38. 38.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 60° (d) 120°
  39. 39.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 120° (b) 115° (c) 60° (d) 125°
  40. 40.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 155° (b) 25° (c) 95° (d) 110°

Answer key

  1. 30°
  2. 115°
  3. 75°
  4. 65°
  5. 85°
  6. 45°
  7. 45°
  8. 120°
  9. 130°
  10. 85°
  11. 10°
  12. 145°
  13. 70°
  14. 95°
  15. 100°
  16. 95°
  17. 120°
  18. 145°
  19. 30°
  20. 40°
  21. 30°
  22. 30°
  23. 40°
  24. 70°
  25. 15°
  26. 125°
  27. 60°
  28. 40°
  29. 130°
  30. 85°
  31. 15°
  32. 90°
  33. 80°
  34. 100°
  35. 85°
  36. 135°
  37. 100°
  38. 120°
  39. 60°
  40. 25°

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