Question

determine the degree measure of one angle of a 30 - sided regular polygon. 5,400° 5,040° 180° 168°

Explanation:

Step1: Find the sum of interior angles

The formula for the sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For \(n = 30\), we have \(S=(30-2)\times180^{\circ}=28\times180^{\circ}=5040^{\circ}\).

Step2: Find the measure of one interior angle

Since it is a regular polygon, all interior angles are equal. The measure of one interior angle \(A=\frac{S}{n}\). Substituting \(S = 5040^{\circ}\) and \(n = 30\), we get \(A=\frac{5040^{\circ}}{30}=168^{\circ}\).

Answer:

\(168^{\circ}\)