Question

applying the polygon interior angle sum theorem
what is the sum of the interior angle measures of a regular decagon?
what is the measure of each interior angle of a regular decagon?

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, \(n = 10\).

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Step2: Find the measure of each interior angle

Since it is a regular decagon, all interior angles are equal. The measure of each interior angle \(A=\frac{(n - 2)\times180^{\circ}}{n}\).

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Answer:

The sum of the interior angle measures of a regular decagon is \(1440^{\circ}\). The measure of each interior angle of a regular decagon is \(144^{\circ}\).