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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 41 · 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 straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 300° (c) 120° (d) 150°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 150° (c) 76° (d) 75°
  3. 3.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 160° (b) 150° (c) 50° (d) 130°
  4. 4.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 95° (b) 155° (c) 85° (d) 110°
  5. 5.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 40° (b) 120° (c) 100° (d) 140°
  6. 6.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 110° (b) 160° (c) 70° (d) 130°
  7. 7.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 270° (c) 90° (d) 110°
  8. 8.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 65° (c) 155° (d) 130°
  9. 9.Two angles of a triangle are 45° and 55°. What is the exterior angle at the third corner? (a) 80° (b) 135° (c) 100° (d) 125°
  10. 10.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 65° (c) 140° (d) 115°
  11. 11.Two angles of a triangle are 75° and 60°. What is the third angle? (a) 105° (b) 120° (c) 135° (d) 45°
  12. 12.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 105° (b) 55° (c) 130° (d) 125°
  13. 13.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) 20° (d) 160°
  14. 14.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) 10° (c) 170° (d) 190°
  15. 15.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 330° (c) 30° (d) 60°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 25° (c) 130° (d) 35°
  17. 17.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 135° (d) 125°
  18. 18.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 20° (b) 65° (c) 160° (d) 135°
  19. 19.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 140° (b) 220° (c) 110° (d) 40°
  20. 20.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 150° (c) 120° (d) 30°
  21. 21.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 260° (b) 80° (c) 160° (d) 100°
  22. 22.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 115° (b) 85° (c) 95° (d) 160°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 60° (d) 75°
  24. 24.Two angles of a triangle are 50° and 65°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 245° (d) 130°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 55° (c) 46° (d) 45°
  26. 26.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 280° (b) 100° (c) 80° (d) 140°
  27. 27.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 45° (d) 135°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 16° (b) 165° (c) 15° (d) 30°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 70° (d) 60°
  30. 30.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 135° (c) 105° (d) 75°
  31. 31.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 150° (d) 65°
  32. 32.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 110° (d) 135°
  33. 33.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) 25° (d) 205°
  34. 34.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 70° (d) 125°
  35. 35.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 70° (b) 125° (c) 250° (d) 110°
  36. 36.Two angles of a triangle are 30° and 95°. What is the third angle? (a) 85° (b) 55° (c) 125° (d) 150°
  37. 37.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 150° (b) 130° (c) 160° (d) 50°
  38. 38.Two angles of a triangle are 45° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 135° (c) 120° (d) 60°
  39. 39.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 21° (c) 200° (d) 20°
  40. 40.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 115° (b) 105° (c) 140° (d) 40°

Answer key

  1. 150°
  2. 75°
  3. 130°
  4. 85°
  5. 40°
  6. 70°
  7. 90°
  8. 130°
  9. 100°
  10. 115°
  11. 45°
  12. 125°
  13. 10°
  14. 10°
  15. 150°
  16. 25°
  17. 100°
  18. 20°
  19. 140°
  20. 150°
  21. 100°
  22. 95°
  23. 75°
  24. 115°
  25. 45°
  26. 100°
  27. 135°
  28. 15°
  29. 60°
  30. 105°
  31. 145°
  32. 115°
  33. 25°
  34. 70°
  35. 70°
  36. 55°
  37. 130°
  38. 120°
  39. 20°
  40. 40°

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