Question

question 4 of 10
the sum of the measures of the interior angles of a polygon with n sides is

a. (n - 3)3600°
b. (n - 2)360°
c. (n - 2)90°
d. (n - 2)180°
e. (n - 3)180°

Explanation:

Step1: Recall polygon - triangle relation

We know that any polygon can be divided into $(n - 2)$ non - overlapping triangles by drawing diagonals from one vertex.

Step2: Use triangle angle - sum property

The sum of the interior angles of a triangle is $180^{\circ}$.

Step3: Calculate polygon interior angle sum

Since a polygon with $n$ sides can be divided into $(n - 2)$ triangles, the sum of the interior angles of a polygon with $n$ sides is $(n - 2)\times180^{\circ}$.

Answer:

D. $(n - 2)180^{\circ}$