Question

what is the angle measure of any interior angle in a regular polygon with 14 sides? round your answer to the nearest tenth.

Explanation:

Step1: Use the formula for the sum of interior angles

The formula for the sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\), where \(n = 14\).

$$S=(14 - 2)\times180^{\circ}=12\times180^{\circ}=2160^{\circ}$$

Step2: Find the measure of one interior angle

Since it is a regular polygon, all interior angles are equal. So, the measure of one interior angle \(A=\frac{S}{n}\).

$$A=\frac{2160^{\circ}}{14}\approx154.3^{\circ}$$

Answer:

\(154.3\)