How do you find the measure of each interior angle of a polygon?

Jan 22, 2016

Without more information, you can only find the value of the interior angles of a regular polygon. Using the equation is $\frac{\left(n - 2\right) {180}^{\circ}}{n}$ where $n$ is the number of sides of the regular polygon

Explanation:

A regular polygon refers to a multi-sided convex figure where all sides are equal in length and all angles have equal degree measures.  The regular triangle has 3 interior angles of ${60}^{\circ}$ and 3 exterior angles of ${120}^{\circ}$. The exterior angle have a sum of ${360}^{\circ} = \left(3\right) {120}^{\circ}$

The square has 4 interior angles of ${90}^{o}$ and 4 exterior angles of ${90}^{\circ}$. The exterior angles have a sum of ${360}^{\circ} = \left(4\right) {90}^{\circ}$.

The pentagon has 5 interior angles of ${108}^{o}$ and 5 exterior angles of ${72}^{\circ}$. The exterior angles have a sum of ${360}^{\circ} = \left(5\right) {72}^{\circ}$.

In order to find the value of the interior angle of a regular polygon, the equation is $\frac{\left(n - 2\right) {180}^{\circ}}{n}$ where n is the number of sides of the regular polygon.

Triangle: $\text{ } \frac{\left(3 - 2\right) {180}^{\circ}}{3} = {60}^{\circ}$

Square $\text{ } \frac{\left(4 - 2\right) {180}^{\circ}}{4} = {90}^{\circ}$

Pentagon $\text{ } \frac{\left(5 - 2\right) {180}^{\circ}}{5} = {108}^{\circ}$