Constructing a line given two other lines, two angles, and a distance.

Question

Two non parallel lines $l$ and $m$ are given. For given two angles $A$ and $B$ we have to construct a line $n$ such that it makes angles $A$ and $B$ with lines $l$ and $m$ respectively. Line $n$ intersects $l$ and $m$ at points $P$ and $Q$ respectively. The length $p$ of $PQ$ is given.

Answer 1

you have been given to much information :)

The angle between l and m is not independent.

it is an ASA construction

• let the base be $PQ$ (has a given length)
• let $R$ be the point where l and m intersect
• $ \angle RPQ $ is $ \angle A $
• $ \angle RQP $ is $ \angle B $

Maybe easiest is to first construct a dummy triangle $P'Q'R'$ and than transport $R'$ to $R$, and so on

Good luck.