Question

question 15 of 27 what is the measure of each interior angle of a regular hexagon? a. 180o b. 60o c. 120o d. 144o

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 \( S=(n - 2)\times180^{\circ} \). For a hexagon, \( n = 6 \).

Step2: Calculate the sum of interior angles of a hexagon

Substitute \( n = 6 \) into the formula: \( S=(6 - 2)\times180^{\circ}=4\times180^{\circ} = 720^{\circ} \).

Step3: Find the measure of each interior angle of a regular hexagon

In a regular polygon, all interior angles are equal. So, each interior angle \( \theta=\frac{S}{n} \). Substitute \( S = 720^{\circ} \) and \( n = 6 \): \( \theta=\frac{720^{\circ}}{6}=120^{\circ} \).

Answer:

C. 120°