Question

26
for a regular polygon with 10 sides, find the measure of each individual interior angle:
(remember, all interior angles in regular polygons are congruent)
each interior angle =

degrees.

Explanation:

Step1: Use the formula for the sum of interior angles

The formula for the sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For \(n = 10\), we have \(S=(10 - 2)\times180^{\circ}\).

$$S=8\times180^{\circ}=1440^{\circ}$$

Step2: Find the measure of each interior angle

Since all interior angles in a regular polygon are congruent, divide the sum \(S\) by \(n\). Each interior angle \(A=\frac{S}{n}\). Substitute \(S = 1440^{\circ}\) and \(n = 10\) into the formula.

$$A=\frac{1440^{\circ}}{10}=144^{\circ}$$

Answer:

\(144\)