Draw $\angle POQ$ of measure 75° and find its line of symmetry.

The steps below are used to construct an angle of 75° and its line of symmetry:

1. Draw a line with the points O and Q marked on it. Draw an arc with a convenient radius, with O at the centre. Let this intersect line l at R.
2. Draw an arc with R as the centre and the same radius as before, intersecting the previously drawn arc at S.
3. Draw an arc that intersects the other arc at point T as shown in the figure, using the same radius as before and S as the centre.
4. Using S and T as the centres, draw an arc with the same radius so that it intersects at U.
5. Join OU. Let V be where it crosses the arc. Draw arcs with a radius of more than 1/2 SV using S and V as the centres now. Let P be the point where these intersect. Join OP. The ray is now forming 75° with line l in OP.
6. Let this ray intersects our major arc at point W. Draw arcs with a radius greater than 1 / 2 RW in the interior angle of 75^o using R and W as the centres. Let X be the point where these intersect. Join OX.

The symmetry line for the $\angle POQ={75}^{°}$ is labelled as OX.