Question

The number of sides of a regular polygon whose each interior angle is of $135°$:

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is C

$8$

The explanation for the correct option:

The formula for the sum $\mathrm{S}$ of $\mathrm{n}$ interior angles of a $\mathrm{n}$ sided polygon, $\mathrm{S}=\left(\mathrm{n}-2\right)\times 180°$
Since the polygon is regular all its interior angles are the same,

$\therefore$ The Sum of them$=135°\times \mathrm{n}$
$\Rightarrow \left(\mathrm{n}-2\right)\times 180=135\times \mathrm{n}$

$\begin{array}{rcl}180\mathrm{n}-360& =& 135\mathrm{n}\\ 180\mathrm{n}-135\mathrm{n}& =& 360\\ 45\mathrm{n}& =& 360\\ \mathrm{n}& =& \frac{360}{45}\\ \mathrm{n}& =& 8\end{array}$

So, the number of sides in this polygon is '$8$'

Therefore, the correct option is C.