Question

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

Explanation:

Step1: Find 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 a quadrilateral (\(n = 4\)), the sum is \((4 - 2)\times180^{\circ}=360^{\circ}\).

Step2: Calculate the measure of each interior angle

Since it is a regular polygon (all angles are equal), divide the sum by the number of sides. So, each interior angle is \(\frac{360^{\circ}}{4}=90^{\circ}\)

Answer:

\(90^{\circ}\)