Question

the sum of the interior angles of a pentagon is ______.
○ 180°
○ 540°
○ 360°
○ 270°

Explanation:

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

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

Step2: Determine the number of sides of a 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 \( S=(5 - 2)\times180^{\circ} \).
First, calculate \( 5-2 = 3 \), then \( 3\times180^{\circ}=540^{\circ} \).

Answer:

540° (the option corresponding to 540°)