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.

• A. ${100}^o$
• B. ${115}^o$
• C. ${95}^o$
• D. ${105}^o$

Answer 1

The correct option is D

${105}^o$

Given AB is the side of a regular octagon

$\Rightarrow$ $\angle AOB$ = $\frac{360}{8}={45}^o$

Given BC is the side of a regular hexagon

$\Rightarrow$ $\angle BOC$ = $\frac{360}{6}={60}^o$

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

= ${45}^o+{60}^o={105}^o$