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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 22 · 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 40° and 110°. What is the third angle? (a) 70° (b) 150° (c) 30° (d) 140°
  2. 2.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 60° (b) 110° (c) 130° (d) 120°
  3. 3.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 56° (c) 235° (d) 55°
  4. 4.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 270° (b) 160° (c) 90° (d) 110°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 41° (b) 40° (c) 80° (d) 140°
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 200° (c) 100° (d) 20°
  7. 7.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 125° (c) 55° (d) 115°
  8. 8.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 125° (b) 110° (c) 235° (d) 55°
  9. 9.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°
  10. 10.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 30° (b) 55° (c) 150° (d) 155°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 40° (d) 100°
  12. 12.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 310° (b) 130° (c) 40° (d) 50°
  13. 13.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 145° (b) 65° (c) 100° (d) 115°
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 115° (c) 130° (d) 66°
  15. 15.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 150° (b) 70° (c) 100° (d) 110°
  16. 16.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 30° (c) 60° (d) 40°
  17. 17.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 40° (c) 140° (d) 100°
  18. 18.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 35° (d) 55°
  19. 19.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 30° (c) 60° (d) 150°
  20. 20.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) 170° (c) 10° (d) 190°
  21. 21.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 20° (d) 80°
  22. 22.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 160° (c) 95° (d) 85°
  23. 23.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 46° (b) 135° (c) 225° (d) 45°
  24. 24.Two angles of a triangle are 75° and 60°. What is the exterior angle at the third corner? (a) 45° (b) 105° (c) 135° (d) 120°
  25. 25.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 20° (c) 40° (d) 30°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 56° (c) 125° (d) 55°
  27. 27.Two angles of a triangle are 55° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 125° (c) 105° (d) 75°
  28. 28.Two angles of a triangle are 25° and 60°. What is the third angle? (a) 85° (b) 120° (c) 155° (d) 95°
  29. 29.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 115° (d) 30°
  30. 30.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 270° (c) 90° (d) 155°
  31. 31.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 95° (b) 160° (c) 115° (d) 85°
  32. 32.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 110° (b) 70° (c) 290° (d) 20°
  33. 33.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) 25° (d) 130°
  34. 34.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 30° (c) 60° (d) 120°
  35. 35.Two angles of a triangle are 40° and 95°. What is the exterior angle at the third corner? (a) 140° (b) 45° (c) 85° (d) 135°
  36. 36.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 95° (b) 275° (c) 5° (d) 85°
  37. 37.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 140° (c) 40° (d) 50°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 110° (b) 70° (c) 35° (d) 45°
  39. 39.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 75° (c) 105° (d) 15°
  40. 40.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 120° (b) 100° (c) 40° (d) 140°

Answer key

  1. 30°
  2. 120°
  3. 55°
  4. 90°
  5. 40°
  6. 100°
  7. 125°
  8. 55°
  9. 20°
  10. 150°
  11. 40°
  12. 130°
  13. 65°
  14. 65°
  15. 110°
  16. 30°
  17. 140°
  18. 110°
  19. 120°
  20. 10°
  21. 80°
  22. 95°
  23. 45°
  24. 135°
  25. 20°
  26. 55°
  27. 105°
  28. 95°
  29. 150°
  30. 90°
  31. 85°
  32. 110°
  33. 25°
  34. 60°
  35. 135°
  36. 95°
  37. 100°
  38. 35°
  39. 30°
  40. 40°

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