Question

How many sides does a regular polygon have if each interior angle measures 162 degrees.

Answer 1

The number of sides of the polygon is denoted by n

.Then we have the relation

`(n-2)*180=162n`

On solving this,

`180n-360=162n`

Then,

`\begin{gathered} 180n-162n=360 \\ 18n=360 \\ n=(360)/(18) \\ n=20 \end{gathered}`

Hence the number of sides is 20.