Question

find the measure of each interior angle of the regular polygon. the measure of each interior angle is

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a triangle (\(n = 3\)), the sum is \((3 - 2)\times180^{\circ}=180^{\circ}\).

Step2: Since it's a regular polygon (equilateral triangle)

In a regular triangle (all sides and angles are equal), each interior angle \(\theta=\frac{(n - 2)\times180^{\circ}}{n}\). Substituting \(n = 3\), we get \(\theta=\frac{(3 - 2)\times180^{\circ}}{3}\).

Step3: Calculate the value

\(\theta=\frac{1\times180^{\circ}}{3}=60^{\circ}\)

Answer:

\(60\)