Question

question 27 of 27 which of the following can be used to find the sum of the interior angles for any regular polygon? a. subtract 2 from the number of sides and multiply the difference by 180 b. multiply the number of sides by 180 c. add 1 to the number of sides and multiply the sum by 180 d. divide the number of sides by 180

Explanation:

The formula for the sum of the interior angles of a polygon is based on the number of sides (\(n\)). A polygon can be divided into \((n - 2)\) triangles, and each triangle has an interior angle sum of \(180^\circ\). So the sum \(S\) of the interior angles of a polygon is \(S=(n - 2)\times180^\circ\), which means we subtract 2 from the number of sides and multiply the difference by 180. Option B would overcount, option C and D do not follow the correct geometric derivation for the sum of interior angles of a polygon.

Answer:

A. Subtract 2 from the number of sides and multiply the difference by 180