Question

how many degrees does each interior angle of a regular pentagon measure? a. 150 degrees b. 108 degrees c. 120 degrees d. 90 degrees

Explanation:

Step1: Use the formula for the sum of interior angles

The formula for the sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a pentagon, \(n = 5\). So \(S=(5 - 2)\times180^{\circ}=3\times180^{\circ}=540^{\circ}\)

Step2: Find the measure of each interior angle

Since it is a regular pentagon, all interior angles are equal. Let each interior angle be \(x\). Then \(x=\frac{S}{n}\). Substitute \(S = 540^{\circ}\) and \(n = 5\), we get \(x=\frac{540^{\circ}}{5}=108^{\circ}\)

Answer:

B. 108 degrees