Question

a bumper pool table is shaped like a regular octagon. find the measure of each interior angle and each exterior angle.

Explanation:

Step1: Recall interior angle formula

For an \(n\)-sided polygon, sum of interior angles is \((n-2)\times180^\circ\). For octagon, \(n=8\).
Sum = \((8-2)\times180^\circ = 6\times180^\circ = 1080^\circ\)

Step2: Calculate each interior angle

Divide total by number of angles (\(n=8\)).
Each interior angle = \(\frac{1080^\circ}{8} = 135^\circ\)

Step3: Recall exterior angle property

Sum of exterior angles of any polygon is \(360^\circ\).

Step4: Calculate each exterior angle

Divide total by number of sides (\(n=8\)).
Each exterior angle = \(\frac{360^\circ}{8} = 45^\circ\)

Answer:

Each interior angle measures \(135^\circ\), and each exterior angle measures \(45^\circ\).