Question

which statements are true about the regular polygon? select three options. the sum of the measures of the interior angles is 900° each interior angle measures 108° all of the angles are congruent. the polygon is a regular hexagon. the sum of the measures of the interior angles is 180(5 - 2)°

Explanation:

Step1: Calculate the sum of interior angles

The formula for the sum of interior angles of a polygon is \(S = 180(n - 2)\), where \(n\) is the number of sides. For a pentagon (\(n=5\)), \(S=180\times(5 - 2)=540^{\circ}\). But \(180\times(5 - 2)\) is a correct formula application.

Step2: Calculate each interior angle of a regular pentagon

For a regular pentagon, each interior angle \(\theta=\frac{180(n - 2)}{n}\). Substituting \(n = 5\), \(\theta=\frac{180\times(5 - 2)}{5}=\frac{540}{5}=108^{\circ}\).

Step3: Properties of a regular polygon

In a regular polygon, all sides and all angles are congruent. A pentagon has \(n = 5\) sides, not \(n=6\) (which is a hexagon).

Answer:

• Each interior angle measures \(108^{\circ}\)
• All of the angles are congruent
• The sum of the measures of the interior angles is \(180(5 - 2)^{\circ}\)