Question

question
what is the sum of the interior angles of a 16 - gon?
answer attempt 1 out of 2

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 \( S=(n - 2)\times180^{\circ} \).

Step2: Identify the number of sides \( n \) for a 16 - gon

For a 16 - gon, the number of sides \( n = 16 \).

Step3: Substitute \( n = 16 \) into the formula

Substitute \( n = 16 \) into the formula \( S=(n - 2)\times180^{\circ} \). We get \( S=(16 - 2)\times180^{\circ} \).

Step4: Calculate the value

First, calculate \( 16-2 = 14 \). Then, multiply \( 14\times180^{\circ} \). \( 14\times180^{\circ}=2520^{\circ} \).

Answer:

The sum of the interior angles of a 16 - gon is \( 2520^{\circ} \)