req: Constructing angles "on the fly"

Hi ! I'm doing some 2D geometric constructions. I need to construct
lines of known length/angle relative to existing oblique lines of
unknown length/angle.

Specifically:
1)I want to construct a line of given length starting at one end of an
existing line of unknown length/angle and at a given angle to the
latter.
2)I would like to construct a line of given start point/length which
will pass through a second line of unknown length/angle, intersecting
the latter at a given angle.

I'm sure there must be an easy way to do this using polar coords &
"snap from"; but I'm struggling, and would be grateful for the most
elegant solution. Thanks in anticipation. Dave

 

Thanks John
Seems to work fine.
Dave.