which statements are true about the regular polygon? select three options. the sum of the measures of the…

Answer:

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

Explanation:

Step1: Identify the polygon type

The polygon has 5 sides, so it's a pentagon.

Step2: Use interior - angle sum formula

The sum of interior angles of an $n$-sided polygon is $S = 180(n - 2)$. For $n = 5$, $S=180(5 - 2)=540^{\circ}$, so the statement "The sum of the measures of the interior angles is $180(5 - 2)^{\circ}$" is true.

Step3: Calculate each interior - angle measure

For a regular pentagon, each interior angle $\theta=\frac{180(n - 2)}{n}=\frac{180\times(5 - 2)}{5}=108^{\circ}$, so "Each interior angle measures $108^{\circ}$" is true.

Step4: Recall property of regular polygons

In a regular polygon, all angles are congruent, so "All of the angles are congruent" is true. And it's a pentagon not a hexagon, so "The polygon is a regular hexagon" is false.