Chapter 11.5, Problem 5CYU

To determine

To find the measure of an interior angle of the regular polygon with 14 sides.

Answer to Problem 5CYU

Interior angle of the polygon is ${154.3}^{\circ }$

Explanation of Solution

Given:

Regular polygon with 14 sides.

Concept used:

The interior angle of a polygon with n sides is $\frac{\left(n-2\right)\times {180}^{\circ }}{n}$ .

Calculation:

Given,

  $n=14$

Therefore interior angle is,

  $\begin{array}{l}\frac{\left(n-2\right)\times {180}^{\circ }}{n}=\frac{\left(14-2\right)\times {180}^{\circ }}{14}\\ =\frac{12\times {180}^{\circ }}{14}\\ =\frac{{2160}^{\circ }}{14}\\ ={154.2857}^{\circ }\\ \approx {154.3}^{\circ }\end{array}$

Hence interior angle of the polygon is ${154.3}^{\circ }$ .