what is the measure of each angle in a regular decagon?
what is the measure of each angle in a regular decagon?
Answer
Explanation:
Step1: Recall the formula for interior - angle sum
The sum of interior angles of an $n$-sided polygon is $S=(n - 2)\times180^{\circ}$. For a decagon, $n = 10$. $S=(10 - 2)\times180^{\circ}=8\times180^{\circ}=1440^{\circ}$
Step2: Calculate the measure of each interior angle
Since a regular decagon has all angles equal, we divide the sum of interior angles by the number of sides $n$. Each interior angle $\theta=\frac{(n - 2)\times180^{\circ}}{n}=\frac{(10 - 2)\times180^{\circ}}{10}=\frac{8\times180^{\circ}}{10}=144^{\circ}$
Answer:
$144^{\circ}$