Question

a regular pentagon is shown.
what is the sum, in degrees, of the interior angle measures of the pentagon?

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon.

The formula for the sum of the interior angle measures of a polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \).

Step2: Identify the number of sides of the pentagon.

A pentagon has \( n = 5 \) sides.

Step3: Substitute \( n = 5 \) into the formula.

Substitute \( n = 5 \) into \( S=(n - 2)\times180^{\circ} \), we get \( S=(5 - 2)\times180^{\circ} \).

Step4: Calculate the value.

First, calculate \( 5-2 = 3 \), then \( 3\times180^{\circ}=540^{\circ} \).

Answer:

\( 540 \)