Question

find the measure of each interior angle and each exterior angle of a regular 12-gon (a twelve-sided polygon).
measure of each interior angle = \\(\square^\circ\\)
measure of each exterior angle = \\(\square^\circ\\)

Explanation:

Step1: Find the sum of interior angles

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 12 - gon, \(n = 12\). So the sum of interior angles is \((12 - 2)\times180^\circ=10\times180^\circ = 1800^\circ\).

Step2: Find each interior angle

Since it is a regular polygon, all interior angles are equal. So each interior angle \(=\frac{(n - 2)\times180^\circ}{n}\). Substituting \(n = 12\), we get \(\frac{1800^\circ}{12}=150^\circ\).

Step3: Find each exterior angle

The sum of exterior angles of any polygon is \(360^\circ\). For a regular polygon, each exterior angle \(=\frac{360^\circ}{n}\). Substituting \(n = 12\), we get \(\frac{360^\circ}{12}=30^\circ\).

Answer:

Measure of each interior angle \(=\boxed{150}\)°
Measure of each exterior angle \(=\boxed{30}\)°