what is the measure of each angle in a regular polygon with 8 sides?

Explanation:

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

The formula for the sum of the interior angles of a polygon with ( n ) sides is ( S=(n - 2)\times180^{\circ} ). For a regular octagon, ( n = 8 ). [ S=(8 - 2)\times180^{\circ} ]

Step2: Calculate the sum of interior angles

First, calculate ( 8-2 = 6 ). Then multiply by ( 180^{\circ} ): [ S=6\times180^{\circ}=1080^{\circ} ]

Step3: Find the measure of each interior angle

In a regular polygon, all interior angles are equal. So we divide the sum of interior angles by the number of sides ( n ). [ \text{Each angle}=\frac{S}{n}=\frac{1080^{\circ}}{8} ]

Step4: Perform the division

[ \frac{1080^{\circ}}{8}=135^{\circ} ]

Answer:

( 135^{\circ} )