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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 232 · 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 straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 36° (b) 35° (c) 70° (d) 145°
  2. 2.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 80° (d) 100°
  3. 3.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 145° (d) 155°
  4. 4.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°
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 75° (b) 76° (c) 105° (d) 150°
  6. 6.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 160° (b) 70° (c) 130° (d) 50°
  7. 7.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 50° (b) 120° (c) 110° (d) 130°
  8. 8.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 125° (c) 55° (d) 150°
  9. 9.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 95° (b) 115° (c) 85° (d) 150°
  10. 10.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) 10° (c) 190° (d) 170°
  11. 11.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 105° (b) 160° (c) 95° (d) 85°
  12. 12.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 160° (d) 80°
  13. 13.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 150° (c) 30° (d) 60°
  14. 14.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°
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 55° (b) 125° (c) 110° (d) 56°
  16. 16.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 90° (b) 170° (c) 10° (d) 100°
  17. 17.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 120° (b) 105° (c) 135° (d) 60°
  18. 18.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 140° (c) 125° (d) 55°
  19. 19.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 45° (d) 135°
  20. 20.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 70° (d) 35°
  21. 21.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 20° (c) 340° (d) 70°
  22. 22.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 100° (b) 280° (c) 80° (d) 140°
  23. 23.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 105° (b) 155° (c) 100° (d) 25°
  24. 24.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 115° (b) 70° (c) 110° (d) 135°
  25. 25.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 35° (d) 110°
  26. 26.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 130° (b) 105° (c) 50° (d) 125°
  27. 27.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 65° (b) 160° (c) 135° (d) 115°
  28. 28.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 110° (b) 55° (c) 125° (d) 235°
  29. 29.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 5° (c) 10° (d) 95°
  30. 30.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 60° (d) 70°
  31. 31.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 55° (b) 125° (c) 150° (d) 155°
  32. 32.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) 120° (c) 30° (d) 60°
  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) 21° (b) 20° (c) 200° (d) 160°
  34. 34.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 130° (d) 80°
  35. 35.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) 255° (d) 75°
  36. 36.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 70° (b) 105° (c) 145° (d) 110°
  37. 37.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 10° (c) 100° (d) 80°
  38. 38.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 110° (b) 155° (c) 70° (d) 135°
  39. 39.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 85° (d) 86°
  40. 40.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 65° (b) 115° (c) 245° (d) 130°

Answer key

  1. 35°
  2. 80°
  3. 60°
  4. 105°
  5. 75°
  6. 50°
  7. 130°
  8. 55°
  9. 95°
  10. 10°
  11. 85°
  12. 80°
  13. 150°
  14. 100°
  15. 55°
  16. 10°
  17. 60°
  18. 125°
  19. 135°
  20. 70°
  21. 160°
  22. 100°
  23. 25°
  24. 110°
  25. 110°
  26. 50°
  27. 65°
  28. 55°
  29. 10°
  30. 60°
  31. 125°
  32. 120°
  33. 20°
  34. 80°
  35. 75°
  36. 70°
  37. 20°
  38. 110°
  39. 85°
  40. 115°

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