Question

determine if the statement is always, sometimes or never true. there are 300 degrees in the sum of the interior angles of a polygon.
○ always
○ sometimes
○ never

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 (where \( n\geq 3 \) and \( n \) is an integer) is \( S=(n - 2)\times180^{\circ} \).

Step2: Set up the equation and solve for \( n \)

We set \( S = 300^{\circ} \), so we have the equation \( (n - 2)\times180=300 \).
First, divide both sides of the equation by \( 180 \): \( n - 2=\frac{300}{180}=\frac{5}{3}\approx1.67 \).
Then, add 2 to both sides: \( n=\frac{5}{3}+ 2=\frac{5 + 6}{3}=\frac{11}{3}\approx3.67 \).

Since \( n \) (the number of sides of a polygon) must be a positive integer greater than or equal to 3, and \( \frac{11}{3} \) is not an integer, there is no polygon with an integer number of sides whose interior angles sum to \( 300^{\circ} \).

Answer:

never