Question

1. what is the sum of the measures of the interior angles of a 27 - gon?

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 \( S=(n - 2)\times180^{\circ} \), where \( n \) is the number of sides of the polygon.

Step2: Identify the number of sides (\( n \)) for the 27 - gon

For a 27 - gon, the number of sides \( n = 27 \).

Step3: Substitute \( n = 27 \) into the formula

Substitute \( n = 27 \) into the formula \( S=(n - 2)\times180^{\circ} \). We get \( S=(27 - 2)\times180^{\circ} \).
First, calculate \( 27-2 = 25 \). Then, calculate \( 25\times180^{\circ}=4500^{\circ} \).

Answer:

The sum of the measures of the interior angles of a 27 - gon is \( 4500^{\circ} \).