Question

find the measure of each interior angle and each exterior angle of a regular 18 - gon (an eighteen - sided polygon).
measure of each interior angle =
measure of each exterior angle =

Explanation:

Step1: Calculate sum of interior angles

The formula for the sum of interior angles of an n-gon is $(n-2)\times180^\circ$. For $n=18$:
$$(18-2)\times180^\circ = 16\times180^\circ = 2880^\circ$$

Step2: Find each interior angle

Divide total by number of sides:
$$\frac{2880^\circ}{18} = 160^\circ$$

Step3: Find each exterior angle

Sum of exterior angles of any polygon is $360^\circ$. Divide by number of sides:
$$\frac{360^\circ}{18} = 20^\circ$$

Answer:

Measure of each interior angle = $160^\circ$
Measure of each exterior angle = $20^\circ$