Question

what is the measure of each interior angle of the regular polygon pictured below? if necessary, round to the nearest tenth.

Explanation:

Step1: Determine the number of sides

The polygon is a heptagon (7 - sided polygon).

Step2: 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 \(n = 7\), the sum is \((7 - 2)\times180^{\circ}=5\times180^{\circ} = 900^{\circ}\).

Step3: Calculate the measure of each interior angle

Since it is a regular polygon, each interior angle is equal. So each interior angle is \(\frac{(n - 2)\times180^{\circ}}{n}\). Substituting \(n = 7\), we get \(\frac{900^{\circ}}{7}\approx128.6^{\circ}\).

Answer:

\(128.6^{\circ}\)