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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 145 · 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 50° and 90°. What is the exterior angle at the third corner? (a) 130° (b) 40° (c) 140° (d) 90°
  2. 2.Two angles of a triangle are 65° and 40°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 115° (d) 140°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 125° (c) 110° (d) 55°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 20° (c) 100° (d) 80°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 50° (c) 130° (d) 25°
  6. 6.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 115° (b) 140° (c) 40° (d) 105°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 20° (b) 11° (c) 10° (d) 170°
  8. 8.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 100° (d) 155°
  9. 9.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 150° (c) 330° (d) 30°
  10. 10.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 30° (c) 120° (d) 60°
  11. 11.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 165° (b) 35° (c) 15° (d) 160°
  12. 12.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 25° (c) 15° (d) 30°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 210° (b) 30° (c) 75° (d) 105°
  14. 14.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 80° (b) 100° (c) 140° (d) 280°
  15. 15.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 70° (c) 145° (d) 110°
  16. 16.Two angles of a triangle are 45° and 110°. What is the third angle? (a) 70° (b) 135° (c) 25° (d) 155°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 155° (c) 310° (d) 130°
  18. 18.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 115° (b) 155° (c) 65° (d) 140°
  19. 19.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 100° (c) 80° (d) 10°
  20. 20.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 70° (c) 55° (d) 125°
  21. 21.Two angles of a triangle are 20° and 30°. What is the third angle? (a) 160° (b) 50° (c) 150° (d) 130°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 55° (c) 46° (d) 90°
  23. 23.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 115° (b) 130° (c) 245° (d) 65°
  24. 24.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 75° (b) 76° (c) 255° (d) 105°
  25. 25.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 120° (b) 40° (c) 140° (d) 100°
  26. 26.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 90° (b) 270° (c) 155° (d) 115°
  27. 27.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 125° (b) 150° (c) 95° (d) 85°
  28. 28.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 150° (b) 115° (c) 145° (d) 65°
  29. 29.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 155° (b) 25° (c) 65° (d) 335°
  30. 30.Two angles of a triangle are 50° and 90°. What is the third angle? (a) 130° (b) 90° (c) 140° (d) 40°
  31. 31.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 140° (b) 135° (c) 85° (d) 95°
  32. 32.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 150° (b) 55° (c) 155° (d) 125°
  33. 33.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 35° (b) 145° (c) 160° (d) 55°
  34. 34.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 55° (b) 155° (c) 125° (d) 150°
  35. 35.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 115° (d) 145°
  36. 36.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 115° (b) 35° (c) 100° (d) 145°
  37. 37.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 105° (b) 20° (c) 160° (d) 95°
  38. 38.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 85° (b) 95° (c) 130° (d) 135°
  39. 39.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 35° (b) 36° (c) 215° (d) 145°
  40. 40.Two angles of a triangle are 25° and 75°. What is the third angle? (a) 80° (b) 155° (c) 105° (d) 100°

Answer key

  1. 140°
  2. 105°
  3. 55°
  4. 100°
  5. 25°
  6. 140°
  7. 10°
  8. 105°
  9. 150°
  10. 120°
  11. 15°
  12. 15°
  13. 105°
  14. 100°
  15. 110°
  16. 25°
  17. 155°
  18. 115°
  19. 100°
  20. 70°
  21. 130°
  22. 45°
  23. 65°
  24. 75°
  25. 140°
  26. 90°
  27. 95°
  28. 115°
  29. 155°
  30. 40°
  31. 95°
  32. 55°
  33. 35°
  34. 125°
  35. 100°
  36. 35°
  37. 20°
  38. 85°
  39. 35°
  40. 80°

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