what is the measure of each angle in a regular polygon with 6 sides?
what is the measure of each angle in a regular polygon with 6 sides?
Answer
Explanation:
Step1: Recall sum - of - interior - angles 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 $n = 6$, we have $S=(6 - 2)\times180^{\circ}$.
Step2: Calculate the sum of interior angles
$S=(6 - 2)\times180^{\circ}=4\times180^{\circ}=720^{\circ}$.
Step3: Find the measure of each interior angle
Since it is a regular polygon, all interior angles are equal. So each interior angle $\theta=\frac{S}{n}$. Substituting $S = 720^{\circ}$ and $n = 6$, we get $\theta=\frac{720^{\circ}}{6}=120^{\circ}$.
Answer:
$120^{\circ}$