Question

find the measure of an interior angle of a regular hexadecagon (16 - sided polygon). x = ?° hint: sum=(n - 2)180

Explanation:

Step1: Find sum of interior angles

For an $n$-sided polygon, the sum of interior - angles formula is $S=(n - 2)\times180^{\circ}$. Here $n = 16$, so $S=(16 - 2)\times180^{\circ}=14\times180^{\circ}=2520^{\circ}$.

Step2: Calculate measure of one interior angle

Since the hexadecagon is regular, all interior angles are equal. Let the measure of one interior angle be $x$. Then $x=\frac{S}{n}$. Substituting $S = 2520^{\circ}$ and $n = 16$, we get $x=\frac{2520^{\circ}}{16}=157.5^{\circ}$.

Answer:

$157.5$