Transferring an angle from one point to another

In this exercise you are given a point

$Q$ on a given line and three points

$X$ ,

$Y$ and

$Z$ which are not on the line. Your task is to construct a line passing through

$Q$ which makes an angle equal to

$\angle XYZ$ with the given line.

Once you have finished the construction, you can check the answer using the angle tool.

The diagram contains an example of a point

$P$ on the given line (coloured in black) and three points

$A$ ,

$B$ and

$C$ . The orange line through

$P$ makes an angle equal to

$\angle ABC$ with the black line.

Hint. This exercise is explained in Euclid Book I, Proposition 23.