Question

1. find the measure of each interior angle of a regular decagon.

Explanation:

Step1: Recall the formula for sum of interior angles

The sum of interior - angles of a polygon is given by $S=(n - 2)\times180^{\circ}$, where $n$ is the number of sides of the polygon. For a decagon, $n = 10$.
$S=(10 - 2)\times180^{\circ}$

Step2: Calculate the sum of interior angles

$S = 8\times180^{\circ}=1440^{\circ}$

Step3: Find the measure of each interior angle

Since a regular decagon has all interior angles equal, if we let $x$ be the measure of each interior angle, then $x=\frac{S}{n}$. Substituting $S = 1440^{\circ}$ and $n = 10$ into the formula.
$x=\frac{1440^{\circ}}{10}=144^{\circ}$

Answer:

$144^{\circ}$