Chapter 12.3, Problem 13E

To determine

To find : The measure of an interior angle and the measure of an exterior angle for the regular quadrilateral.

Answer to Problem 13E

The measure of an interior angle of regular quadrilateral is ${90}^{\circ }$ and the measure of an exterior angle of a regular quadrilateral is ${90}^{\circ }$ .

Explanation of Solution

Given information : Here, the polygon is regular quadrilateral.

Formula used : All interior angles of a regular polygon are equal and the measure of an interior angle of regular n-gon is $\frac{\left(n-2\right)\times {180}^{\circ }}{n}$

All exterior angles of a regular polygon are equal and the measure of an exterior angle of regular n-gon is ${180}^{\circ }-\frac{\left(n-2\right)\times {180}^{\circ }}{n}$

Calculation :

Here, polygon is regular quadrilateral i.e. $n=4$

Therefore, the measure of an interior angle of regular quadrilateral is

  $\begin{array}{l}\frac{\left(4-2\right)\times {180}^{\circ }}{4}\\ \Rightarrow \frac{2\times {180}^{\circ }}{4}\\ \Rightarrow \frac{{360}^{\circ }}{4}\\ \Rightarrow {90}^{\circ }\end{array}$

The measure of an exterior angle of a regular quadrilateral is

  $\begin{array}{l}{180}^{\circ }-\frac{\left(4-2\right)\times {180}^{\circ }}{4}\\ \Rightarrow {180}^{\circ }-\frac{2\times {180}^{\circ }}{4}\\ \Rightarrow {180}^{\circ }-\frac{{360}^{\circ }}{4}\\ \Rightarrow {180}^{\circ }-{90}^{\circ }\\ \Rightarrow {90}^{\circ }\end{array}$