Question

what is the angle measure of any interior angle in a regular polygon with 14 sides? round your answer to the nearest tenth. 154 °

Explanation:

Step1: Use the formula for the sum of interior angles

The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For \(n = 14\), the sum \(S=(14 - 2)\times180^{\circ}=12\times180^{\circ}=2160^{\circ}\).

Step2: Find the measure of one interior angle

Since the polygon is regular (all angles are equal), divide the sum by the number of sides. Let \(A\) be the measure of one interior angle. Then \(A=\frac{2160^{\circ}}{14}\approx154.3^{\circ}\)

Answer:

\(154.3^{\circ}\)