Find the measure of each of the interior angles of the regular hexagon using the Polygon Interior Angle Sum Theorem.

Answer 1

To find the measure of each interior angle of a regular hexagon using the Polygon Interior Angle Sum Theorem, we first need to determine the total sum of the interior angles in the hexagon.

The formula for the sum of the interior angles of a polygon is:

$$\text{Sum}=(n-2)\times {180}^{\circ }$$

where $n$ is the number of sides in the polygon. A hexagon has $n=6$ sides.

Now, applying the formula:

$$\text{Sum}=(6-2)\times {180}^{\circ }=4\times {180}^{\circ }={720}^{\circ }$$

The sum of the interior angles of a hexagon is ${720}^{\circ }$.

Since we are interested in a regular hexagon, all interior angles are equal. We can find the measure of each interior angle by dividing the total sum by the number of angles (which is equal to the number of sides, $n$):

$$\text{Measure of each interior angle}=\frac{\text{Sum}}{n}=\frac{{720}^{\circ }}{6}={120}^{\circ }$$

Therefore, each interior angle of a regular hexagon measures ${120}^{\circ }$.