Question

How many sides does a regular polygon have if each exterior angle measures 72 degrees? (problem also attached below)thank you ! :)

Answer 1

Solution

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the theorem for exterior angles

The sum of exterior angles of a regular polygon is 360 degrees. This implies that "A regular polygon with n number of sides has the sum of all the exterior angles to be 360 degrees.

From the theorem above,

$72n=360^{\circ}$

STEP 2: find the number of sides

$\begin{gathered} 72n=360^{\circ} \\ Divide\text{ both sides by 72} \\ \frac{72n}{72}=\frac{360^{\circ}}{72} \\ n=5 \end{gathered}$

Hence, the regular polygon has 5 sides