Chapter 11, Problem 7PT

To determine

To find:the measure of each interior angles of regular of a 16-gon.

Answer to Problem 7PT

  $\text{F}. {157.5}^{\circ }$

Explanation of Solution

Given:

A regular of a 16-gon

And the options are:

  $\begin{array}{l}\text{F}. {157.5}^{\circ }\\ \text{G}. {205.7}^{\circ }\\ \text{H}. {2520}^{\circ }\\ \text{J}. {2880}^{\circ }\end{array}$

Calculation:

As it is known that sum of interior angles of n-gon is $\left(n-2\right){180}^{\circ }$

Therefore, for 16-gon is $\left(16-2\right){180}^{\circ }=14\times {180}^{\circ }={2520}^{\circ }$

Let x be the one angle.

Since all angles of 16gon are same.

Therefore,

  $\begin{array}{l}16x={2520}^{\circ }\\ \Rightarrow x=\frac{2520c}{16}={157.5}^{\circ }\end{array}$

Hence each angle of regular 16-gon is ${157.5}^{\circ }$ .

Thus, the correct option is F.