Question

find the measure of one interior angle in the regular polygon. the measure of each interior angle is □°. (type an integer.)

Explanation:

Step1: Recall the formula for the sum of interior angles

The sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a regular decagon (\(n = 10\)), \(S=(10 - 2)\times180^{\circ}=8\times180^{\circ}=1440^{\circ}\).

Step2: Calculate the measure of one interior angle

Since it is a regular polygon, all interior angles are equal. So, one interior angle \(A=\frac{S}{n}\). Substituting \(S = 1440^{\circ}\) and \(n = 10\), we get \(A=\frac{1440^{\circ}}{10}=144^{\circ}\).

Answer:

\(144\)