the diagram shows a regular polygon. what is the value of x? write your answer as an integer or as a decimal…

Explanation:

Step1: Recall polygon - angle formula

The sum of interior angles of a polygon is given by $S=(n - 2)\times180^{\circ}$, where $n$ is the number of sides. For a hexagon, $n = 6$. So, $S=(6 - 2)\times180^{\circ}=4\times180^{\circ}=720^{\circ}$.

Step2: Find the measure of each interior angle

Since it is a regular hexagon, all interior angles are equal. Let the measure of each interior angle be $x$. We know that for a regular polygon with $n$ sides, the measure of each interior angle $x=\frac{(n - 2)\times180^{\circ}}{n}$. Substituting $n = 6$ into the formula: $x=\frac{(6 - 2)\times180^{\circ}}{6}=\frac{4\times180^{\circ}}{6}=120^{\circ}$.

Answer:

$120$