Question

In the given figure AB is the side of a regular octagon and BC is the side of a regular hexagon. Find $\angle$ AOC.

Answer 1

Given AB is the side of a regular octagon.

$\Rightarrow$ $\angle AOB$ = $\frac{360}{8}={45}^o$ (1 mark)

Given BC is the side of a regular hexagon.

$\Rightarrow$ $\angle BOC$ = $\frac{360}{6}={60}^o$ (1 mark)

$\angle AOC$ = $\angle AOB$ + $\angle BOC$

= ${45}^o+{60}^o={105}^o$ (1 mark)