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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 188 · 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 30°. What is the third angle? (a) 100° (b) 150° (c) 130° (d) 80°
  2. 2.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 40° (c) 130° (d) 50°
  3. 3.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 340° (c) 70° (d) 160°
  4. 4.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 265° (c) 95° (d) 85°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 60° (c) 30° (d) 150°
  6. 6.Two angles of a triangle are 30° and 75°. What is the third angle? (a) 75° (b) 105° (c) 150° (d) 255°
  7. 7.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 125° (c) 35° (d) 55°
  8. 8.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 30° (d) 150°
  9. 9.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 65° (b) 155° (c) 140° (d) 115°
  10. 10.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 46° (b) 45° (c) 135° (d) 90°
  11. 11.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 70° (b) 100° (c) 110° (d) 150°
  12. 12.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 115° (c) 50° (d) 25°
  13. 13.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 100° (b) 35° (c) 115° (d) 145°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 125° (c) 56° (d) 55°
  15. 15.Two angles of a triangle are 60° and 75°. What is the exterior angle at the third corner? (a) 120° (b) 105° (c) 135° (d) 45°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 10° (b) 170° (c) 11° (d) 20°
  17. 17.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 50° (b) 51° (c) 230° (d) 130°
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 170° (c) 95° (d) 85°
  19. 19.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 60° (b) 155° (c) 85° (d) 120°
  20. 20.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 100° (d) 135°
  21. 21.Two angles of a triangle are 25° and 115°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 65° (d) 155°
  22. 22.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 60° (b) 240° (c) 61° (d) 120°
  23. 23.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 140° (b) 220° (c) 80° (d) 40°
  24. 24.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°
  25. 25.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 140° (d) 100°
  26. 26.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 260° (b) 80° (c) 100° (d) 160°
  27. 27.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 100° (d) 230°
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 40° (c) 80° (d) 41°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 140° (c) 40° (d) 70°
  30. 30.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 115° (b) 270° (c) 155° (d) 90°
  31. 31.Two angles of a triangle are 35° and 20°. What is the third angle? (a) 160° (b) 145° (c) 125° (d) 55°
  32. 32.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 80° (b) 10° (c) 110° (d) 170°
  33. 33.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 21° (c) 20° (d) 160°
  34. 34.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 50° (c) 80° (d) 130°
  35. 35.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 155° (d) 70°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 130° (b) 65° (c) 66° (d) 115°
  37. 37.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 40° (b) 21° (c) 160° (d) 20°
  38. 38.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 115° (b) 295° (c) 25° (d) 65°
  39. 39.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 155° (c) 105° (d) 80°
  40. 40.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 155° (b) 105° (c) 75° (d) 130°

Answer key

  1. 100°
  2. 65°
  3. 160°
  4. 85°
  5. 75°
  6. 75°
  7. 70°
  8. 150°
  9. 65°
  10. 45°
  11. 110°
  12. 50°
  13. 35°
  14. 55°
  15. 135°
  16. 10°
  17. 50°
  18. 85°
  19. 120°
  20. 125°
  21. 140°
  22. 60°
  23. 40°
  24. 150°
  25. 100°
  26. 100°
  27. 130°
  28. 40°
  29. 70°
  30. 90°
  31. 125°
  32. 10°
  33. 20°
  34. 80°
  35. 135°
  36. 65°
  37. 20°
  38. 115°
  39. 100°
  40. 75°

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