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: Use the formula for the sum of interior angles of a polygon

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 \(S=(5 - 2)\times180^{\circ}=540^{\circ}
eq900^{\circ}\).

Step2: Calculate the measure of each interior angle of a regular pentagon

For a regular pentagon (\(n = 5\)), the measure of each interior angle \(A=\frac{(n - 2)\times180^{\circ}}{n}\). Substitute \(n = 5\) into the formula: \(A=\frac{(5 - 2)\times180^{\circ}}{5}=\frac{3\times180^{\circ}}{5}=108^{\circ}\).

Step3: Analyze the properties of a regular polygon

A regular polygon has all sides and all angles congruent. Since it is a pentagon (5 - sided polygon), not a hexagon (6 - sided polygon). And the sum of interior angles for \(n = 5\) is \(180\times(5 - 2)\) according to the formula \(S=(n - 2)\times180^{\circ}\).

Answer:

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