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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 559 · 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 50°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 120° (d) 130°
  2. 2.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 95° (b) 130° (c) 45° (d) 135°
  3. 3.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 95° (b) 140° (c) 135° (d) 85°
  4. 4.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 120° (b) 20° (c) 160° (d) 80°
  5. 5.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 130° (c) 125° (d) 55°
  6. 6.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 100° (c) 80° (d) 10°
  7. 7.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 150° (b) 45° (c) 135° (d) 75°
  8. 8.Two angles of a triangle are 25° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 155° (c) 105° (d) 75°
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 25° (c) 310° (d) 130°
  10. 10.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 135° (b) 160° (c) 45° (d) 155°
  11. 11.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 95° (b) 130° (c) 85° (d) 145°
  12. 12.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 145° (c) 110° (d) 55°
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 55° (b) 110° (c) 125° (d) 56°
  14. 14.Two angles of a triangle are 40° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 140° (c) 70° (d) 110°
  15. 15.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 155° (d) 150°
  16. 16.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 120° (b) 90° (c) 150° (d) 30°
  17. 17.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 150° (d) 115°
  18. 18.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 125° (c) 65° (d) 115°
  19. 19.Two angles of a triangle are 25° and 90°. What is the third angle? (a) 90° (b) 65° (c) 155° (d) 115°
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 75° (c) 76° (d) 105°
  21. 21.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 10° (c) 85° (d) 95°
  22. 22.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 195° (c) 16° (d) 165°
  23. 23.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 255° (b) 150° (c) 75° (d) 105°
  24. 24.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 150° (b) 100° (c) 80° (d) 130°
  25. 25.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 45° (b) 135° (c) 120° (d) 105°
  26. 26.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 125° (c) 35° (d) 70°
  27. 27.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 340° (b) 20° (c) 160° (d) 70°
  28. 28.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 100° (d) 80°
  29. 29.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 145° (d) 100°
  30. 30.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) 335° (c) 25° (d) 155°
  31. 31.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 50° (b) 130° (c) 110° (d) 120°
  32. 32.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 70° (b) 105° (c) 145° (d) 110°
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 130° (c) 65° (d) 115°
  34. 34.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 45° (c) 46° (d) 225°
  35. 35.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 105° (b) 125° (c) 75° (d) 130°
  36. 36.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 105° (b) 120° (c) 75° (d) 135°
  37. 37.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 265° (d) 86°
  38. 38.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 120° (b) 145° (c) 60° (d) 155°
  39. 39.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 70° (b) 150° (c) 110° (d) 140°
  40. 40.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 30° (c) 15° (d) 105°

Answer key

  1. 110°
  2. 45°
  3. 85°
  4. 20°
  5. 125°
  6. 20°
  7. 45°
  8. 105°
  9. 155°
  10. 135°
  11. 95°
  12. 110°
  13. 55°
  14. 70°
  15. 55°
  16. 150°
  17. 95°
  18. 115°
  19. 65°
  20. 75°
  21. 10°
  22. 15°
  23. 105°
  24. 100°
  25. 45°
  26. 70°
  27. 160°
  28. 100°
  29. 115°
  30. 155°
  31. 50°
  32. 110°
  33. 65°
  34. 45°
  35. 75°
  36. 75°
  37. 85°
  38. 60°
  39. 70°
  40. 30°

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