Question

question 6 of 10
the sum of the measures of the interior angles of a polygon with n sides is

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

Explanation:

Step1: Recall polygon - angle formula

The sum of the interior - angle measures of a polygon with \(n\) sides can be derived by dividing the polygon into \((n - 2)\) non - overlapping triangles.

Step2: Know the angle - sum of a triangle

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

Step3: Calculate the sum for the polygon

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

Answer:

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