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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 242 · 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 60° and 20°. What is the third angle? (a) 160° (b) 80° (c) 100° (d) 120°
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 75° (c) 150° (d) 105°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 51° (c) 50° (d) 100°
  4. 4.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 60° (b) 300° (c) 150° (d) 120°
  5. 5.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 30° (b) 50° (c) 160° (d) 150°
  6. 6.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) 10° (c) 80° (d) 100°
  7. 7.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 310° (c) 40° (d) 130°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 110° (c) 35° (d) 70°
  9. 9.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 110° (c) 95° (d) 85°
  10. 10.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 35° (d) 25°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 30° (c) 60° (d) 150°
  12. 12.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 50° (b) 230° (c) 130° (d) 100°
  13. 13.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 125° (b) 115° (c) 120° (d) 60°
  14. 14.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 220° (c) 40° (d) 140°
  15. 15.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 145° (b) 155° (c) 120° (d) 60°
  16. 16.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 76° (c) 75° (d) 255°
  17. 17.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 70° (c) 110° (d) 55°
  18. 18.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 145° (c) 125° (d) 55°
  19. 19.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 65° (c) 100° (d) 115°
  20. 20.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 80° (c) 10° (d) 50°
  21. 21.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 61° (c) 30° (d) 60°
  22. 22.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 110° (c) 70° (d) 100°
  23. 23.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 70° (b) 140° (c) 110° (d) 150°
  24. 24.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 91° (b) 90° (c) 135° (d) 270°
  25. 25.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 160° (d) 150°
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 100° (c) 20° (d) 200°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 70° (b) 35° (c) 36° (d) 145°
  28. 28.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 20° (c) 200° (d) 160°
  29. 29.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 75° (c) 135° (d) 105°
  30. 30.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 45° (c) 91° (d) 135°
  31. 31.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 125° (b) 110° (c) 55° (d) 235°
  32. 32.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 80° (b) 155° (c) 125° (d) 25°
  33. 33.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 125° (d) 105°
  34. 34.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 66° (b) 245° (c) 65° (d) 115°
  35. 35.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°
  36. 36.Two angles of a triangle are 45° and 85°. What is the third angle? (a) 130° (b) 50° (c) 95° (d) 135°
  37. 37.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 140° (c) 120° (d) 80°
  38. 38.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 105° (b) 35° (c) 145° (d) 110°
  39. 39.Two angles of a triangle are 70° and 45°. What is the third angle? (a) 110° (b) 115° (c) 135° (d) 65°
  40. 40.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 150° (b) 145° (c) 65° (d) 115°

Answer key

  1. 100°
  2. 75°
  3. 50°
  4. 120°
  5. 30°
  6. 100°
  7. 130°
  8. 35°
  9. 95°
  10. 25°
  11. 75°
  12. 130°
  13. 60°
  14. 140°
  15. 120°
  16. 75°
  17. 55°
  18. 55°
  19. 115°
  20. 50°
  21. 60°
  22. 110°
  23. 70°
  24. 90°
  25. 50°
  26. 100°
  27. 35°
  28. 20°
  29. 75°
  30. 90°
  31. 55°
  32. 25°
  33. 130°
  34. 65°
  35. 45°
  36. 50°
  37. 100°
  38. 145°
  39. 65°
  40. 115°

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