Question

calculate the measure of each interior angle of a regular decagon. ———— degrees

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 decagon (\(n = 10\)), the sum \(S=(10 - 2)\times180^{\circ}=8\times180^{\circ}=1440^{\circ}\).

Step2: Calculate the measure of each interior angle

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

Answer:

\(144\)