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It is possible to construct an infinite number of lines through any line at a given point. You will not be able to physically draw them, but a filled in circle will all have rays that intersect the line at the same point.
Complement of a given angle = (90 - given angle) Supplement of a given angle = (180 - given angle)
Yes. That's always possible, but there's only one of them.
With the information that is available from the question, it is impossible.
Adjust the compass to the given line segment then construct the circle.