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Question:

Construct an angle of 45° from a horizontal line and justify the construction.

Solution:

  1. Draw a ray OX.
  2. Cut an arc from point O of any length.
  3. Cut two arcs A and B on the previous arc (which are at the angle of 60° and 120°).
  4. Cut two arc from points A and B and their point of intersection is C.
  5. Join O−C. ∠COX is 90°.
  6. Bisect ∠COX through cutting two arcs from D and E, their point of intersection is F.
  7. Join F−O, ∠FOX is 45°