what is the measure of each angle in a regular polygon with 9 sides?
what is the measure of each angle in a regular polygon with 9 sides?
Answer
Explanation:
Step1: Recall the formula for sum of interior - angles.
The sum of interior angles of a polygon with (n) sides is (S=(n - 2)\times180^{\circ}). Here (n = 9), so (S=(9 - 2)\times180^{\circ}=7\times180^{\circ}=1260^{\circ}).
Step2: Find the measure of each angle.
Since the polygon is regular, all interior angles are equal. Let (x) be the measure of each interior angle. Then (x=\frac{S}{n}). Substituting (S = 1260^{\circ}) and (n = 9), we get (x=\frac{1260^{\circ}}{9}=140^{\circ}).
Answer:
(140^{\circ})