Question

In the given figure, $AB$ is a side of a regular hexagon and $AC$ is a side a regular eight sided polygon, Find:
$\angle BOC$

Answer 1

As $AB$ is the side of a hexagon so the
$\angle AOB=\frac{{360}^o}{6}={60}^o$
$AC$ is the side of an eight sided polygon so,
$\angle AOC=\frac{{360}^o}{8}={45}^o$
From the given figure we can see that :
$\angle BOC=\angle AOB+\angle AOC={60}^o+{45}^o={105}^o$