Question

If each interior angle of a regular polygon is $135°$ how many sides does it have ?

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is C

$8$

As we know that the measures of each interior angles of a polygon having $n$ sides is$=\frac{(n-2)\times 180}{n}$

Now the measure of given interior angle is $=135°$

$$\begin{gathered} 135°=\frac{(n-2)\times 180}{n} \\ 135n=180n-360 \\ n=\frac{360}{45}=8 \end{gathered}$$
Hence, the number of sides of a regular polygon is $8$.