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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 97 · 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. 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°
  2. 2.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) 225° (c) 46° (d) 45°
  3. 3.Two angles of a triangle are 75° and 75°. What is the exterior angle at the third corner? (a) 30° (b) 105° (c) 210° (d) 150°
  4. 4.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 85° (b) 130° (c) 95° (d) 145°
  5. 5.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 100° (b) 145° (c) 115° (d) 65°
  6. 6.Two angles of a triangle are 50° and 70°. What is the third angle? (a) 60° (b) 110° (c) 120° (d) 130°
  7. 7.Two angles of a triangle are 50° and 20°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 130° (d) 160°
  8. 8.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 110° (b) 125° (c) 235° (d) 55°
  9. 9.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 145° (c) 155° (d) 60°
  10. 10.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 210° (b) 60° (c) 150° (d) 30°
  11. 11.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 95° (c) 85° (d) 145°
  12. 12.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 125° (d) 55°
  13. 13.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 160° (d) 155°
  14. 14.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 40° (b) 70° (c) 150° (d) 140°
  15. 15.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 110° (b) 130° (c) 70° (d) 120°
  16. 16.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°
  17. 17.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 85° (d) 10°
  18. 18.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 115° (c) 65° (d) 295°
  19. 19.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 100° (c) 80° (d) 40°
  20. 20.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 145° (b) 85° (c) 120° (d) 95°
  21. 21.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 140° (c) 40° (d) 120°
  22. 22.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 145° (b) 55° (c) 160° (d) 20°
  23. 23.Two angles of a triangle are 25° and 65°. What is the exterior angle at the third corner? (a) 270° (b) 155° (c) 115° (d) 90°
  24. 24.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 85° (b) 130° (c) 95° (d) 135°
  25. 25.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 310° (c) 40° (d) 50°
  26. 26.Two angles of a triangle are 40° and 110°. What is the exterior angle at the third corner? (a) 140° (b) 150° (c) 30° (d) 70°
  27. 27.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 165° (c) 15° (d) 16°
  28. 28.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 55° (c) 160° (d) 125°
  29. 29.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 130° (c) 70° (d) 110°
  30. 30.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 65° (b) 105° (c) 140° (d) 115°
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 66° (b) 65° (c) 115° (d) 130°
  32. 32.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 55° (c) 35° (d) 70°
  33. 33.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 35° (b) 110° (c) 145° (d) 105°
  34. 34.Two angles of a triangle are 25° and 145°. What is the third angle? (a) 155° (b) 170° (c) 35° (d) 10°
  35. 35.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 70° (c) 220° (d) 110°
  36. 36.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 50° (c) 80° (d) 260°
  37. 37.Two angles of a triangle are 65° and 25°. What is the third angle? (a) 90° (b) 155° (c) 270° (d) 115°
  38. 38.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 140° (b) 170° (c) 10° (d) 50°
  39. 39.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 95° (c) 160° (d) 85°
  40. 40.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 26° (b) 155° (c) 205° (d) 25°

Answer key

  1. 55°
  2. 45°
  3. 150°
  4. 85°
  5. 65°
  6. 60°
  7. 70°
  8. 55°
  9. 60°
  10. 150°
  11. 85°
  12. 125°
  13. 45°
  14. 140°
  15. 70°
  16. 85°
  17. 10°
  18. 115°
  19. 40°
  20. 95°
  21. 140°
  22. 20°
  23. 90°
  24. 85°
  25. 130°
  26. 150°
  27. 15°
  28. 55°
  29. 110°
  30. 65°
  31. 65°
  32. 70°
  33. 145°
  34. 10°
  35. 110°
  36. 130°
  37. 90°
  38. 10°
  39. 85°
  40. 25°

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