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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 213 · 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 45°. What is the third angle? (a) 135° (b) 95° (c) 85° (d) 130°
  2. 2.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 50° (b) 100° (c) 130° (d) 230°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 310° (c) 130° (d) 155°
  4. 4.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 115° (c) 50° (d) 65°
  5. 5.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 65° (d) 130°
  6. 6.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 95° (c) 35° (d) 120°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 110° (b) 70° (c) 71° (d) 140°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 20° (c) 160° (d) 80°
  9. 9.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 30° (d) 15°
  10. 10.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 50° (c) 51° (d) 130°
  11. 11.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 110° (c) 55° (d) 35°
  12. 12.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°
  13. 13.Two angles of a triangle are 30° and 100°. What is the third angle? (a) 130° (b) 150° (c) 50° (d) 80°
  14. 14.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 70° (c) 50° (d) 40°
  15. 15.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°
  16. 16.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 270° (c) 110° (d) 90°
  17. 17.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 125° (b) 145° (c) 90° (d) 35°
  18. 18.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 135° (b) 45° (c) 130° (d) 95°
  19. 19.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 130° (b) 230° (c) 50° (d) 115°
  20. 20.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 150° (b) 90° (c) 120° (d) 270°
  21. 21.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 30° (b) 150° (c) 100° (d) 110°
  22. 22.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 25° (b) 205° (c) 155° (d) 26°
  23. 23.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 60° (b) 125° (c) 120° (d) 115°
  24. 24.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 65° (b) 115° (c) 100° (d) 145°
  25. 25.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 130° (b) 50° (c) 110° (d) 120°
  26. 26.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) 30° (d) 105°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 40°
  28. 28.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) 330° (c) 150° (d) 30°
  29. 29.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 70° (d) 55°
  30. 30.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 115° (c) 65° (d) 66°
  31. 31.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 25° (c) 155° (d) 335°
  32. 32.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 125° (d) 100°
  33. 33.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 45° (c) 35° (d) 110°
  34. 34.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 80° (c) 100° (d) 125°
  35. 35.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 145° (b) 135° (c) 80° (d) 100°
  36. 36.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 81° (b) 100° (c) 80° (d) 260°
  37. 37.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 100° (d) 80°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 45° (d) 90°
  39. 39.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 115° (d) 105°
  40. 40.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) 160° (d) 20°

Answer key

  1. 85°
  2. 130°
  3. 155°
  4. 50°
  5. 65°
  6. 145°
  7. 70°
  8. 80°
  9. 30°
  10. 50°
  11. 110°
  12. 60°
  13. 50°
  14. 70°
  15. 85°
  16. 90°
  17. 35°
  18. 45°
  19. 50°
  20. 90°
  21. 30°
  22. 25°
  23. 60°
  24. 65°
  25. 50°
  26. 105°
  27. 40°
  28. 150°
  29. 55°
  30. 65°
  31. 155°
  32. 80°
  33. 35°
  34. 80°
  35. 100°
  36. 80°
  37. 100°
  38. 45°
  39. 105°
  40. 20°

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