Chapter 13.4, Problem 5MRE

To determine

To find the each interior angle of a regular hexagon.

Answer to Problem 5MRE

Each interior angle of a regular hexagon is $\frac{2\pi }{3}$ .

Explanation of Solution

Given information:Each interior angle of a interior angle of a regular hexagon.

Calculation: The required angle of a regular hexagon is obtained as,

Hexagon figure is,

  

  $\angle EOD=\frac{2\pi }{6}=\frac{\pi }{6}$

Therefore, it is regular.

  $OE=OD$

In triangle OED,

  $\begin{array}{l}OE=OD\\ \therefore \angle OED=\angle ODE\\ \angle OED+\angle ODE+\angle EOD=\pi \\ 2\angle OED=\pi -\frac{\pi }{3}\\ 2\angle OED=\frac{2\pi }{3}\\ \angle OED=\frac{\pi }{3}\end{array}$

One interior angle of hexagon,

  $\begin{array}{l}\angle FED=2\angle OED\\ \angle FED=\frac{2\pi }{3}\end{array}$

Hence, each interior angle of a regular hexagon is $\frac{2\pi }{3}$ .