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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 46 · 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 60°. What is the third angle? (a) 90° (b) 120° (c) 150° (d) 270°
  2. 2.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 80° (b) 100° (c) 280° (d) 140°
  3. 3.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 70° (b) 110° (c) 160° (d) 130°
  4. 4.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 75° (d) 125°
  5. 5.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 100° (b) 160° (c) 80° (d) 260°
  6. 6.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 130° (b) 50° (c) 230° (d) 51°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 40° (c) 21° (d) 20°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 70° (d) 60°
  9. 9.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 120° (b) 145° (c) 95° (d) 35°
  10. 10.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 160° (b) 170° (c) 10° (d) 30°
  11. 11.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 270° (c) 90° (d) 91°
  12. 12.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 155° (d) 120°
  13. 13.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 115° (c) 65° (d) 140°
  14. 14.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 50° (b) 30° (c) 150° (d) 160°
  15. 15.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 145° (b) 25° (c) 155° (d) 60°
  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) 210° (c) 105° (d) 30°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 86° (c) 170° (d) 95°
  18. 18.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 115° (b) 90° (c) 270° (d) 155°
  19. 19.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 40° (c) 41° (d) 140°
  20. 20.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 140° (c) 60° (d) 120°
  21. 21.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 115° (c) 65° (d) 50°
  22. 22.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 150° (b) 30° (c) 75° (d) 135°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 75° (c) 30° (d) 60°
  24. 24.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 130° (c) 40° (d) 65°
  25. 25.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 145° (c) 60° (d) 120°
  26. 26.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 80° (c) 10° (d) 20°
  27. 27.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 70° (b) 110° (c) 250° (d) 125°
  28. 28.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 125° (b) 80° (c) 135° (d) 100°
  29. 29.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 155° (b) 55° (c) 150° (d) 25°
  30. 30.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 160° (b) 90° (c) 110° (d) 270°
  31. 31.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 26° (c) 25° (d) 155°
  32. 32.Two angles of a triangle are 20° and 55°. What is the third angle? (a) 75° (b) 160° (c) 105° (d) 125°
  33. 33.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 125° (b) 90° (c) 270° (d) 145°
  34. 34.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 125° (b) 110° (c) 55° (d) 235°
  35. 35.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 35° (c) 130° (d) 25°
  36. 36.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 25° (c) 155° (d) 65°
  37. 37.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 30° (c) 140° (d) 40°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 10° (c) 160° (d) 20°
  39. 39.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 150° (c) 30° (d) 60°
  40. 40.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 100° (b) 150° (c) 80° (d) 110°

Answer key

  1. 90°
  2. 100°
  3. 110°
  4. 105°
  5. 80°
  6. 50°
  7. 20°
  8. 60°
  9. 35°
  10. 10°
  11. 90°
  12. 85°
  13. 65°
  14. 30°
  15. 25°
  16. 105°
  17. 85°
  18. 90°
  19. 40°
  20. 60°
  21. 50°
  22. 150°
  23. 75°
  24. 65°
  25. 120°
  26. 20°
  27. 70°
  28. 100°
  29. 25°
  30. 90°
  31. 25°
  32. 105°
  33. 90°
  34. 55°
  35. 25°
  36. 155°
  37. 20°
  38. 10°
  39. 30°
  40. 80°

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