Questions: Fill in the blank so that the resulting statement is true. The sum of the measures of the angles of a polygon with n sides is

Transcript text: Fill in the blank so that the resulting statement is true. The sum of the measures of the angles of a polygon with $n$ sides is $\qquad$

Solution

Solution Steps

To find the sum of the measures of the angles of a polygon with $ n $ sides, we use the formula $(n - 2) \times 180$. This formula is derived from the fact that a polygon can be divided into $(n - 2)$ triangles, and each triangle has an angle sum of 180 degrees.

Step 1: Understanding the Problem

We need to find the sum of the measures of the angles of a polygon with $ n $ sides. The formula for this sum is given by:

\[ \text{Sum of angles} = (n - 2) \times 180 \]

Step 2: Applying the Formula

For a polygon with $ n = 5 $ sides (a pentagon), we substitute $ n $ into the formula:

\[ \text{Sum of angles} = (5 - 2) \times 180 = 3 \times 180 \]

Step 3: Calculating the Result

Now, we perform the multiplication:

\[ 3 \times 180 = 540 \]