Question

What is the diffrence between the interior and the exterior angle of a regular pentagon?

• A. ${72}^o$
• B. ${108}^o$
• C. ${36}^o$
• D. ${30}^o$

Answer 1

The correct option is C ${36}^o$

In the regular pentagon, there are $5$ equal interior angles and $5$ exterior angles also.

Now, let the interior angles be $y$ and exterior angles be $x$

So,
Sum of all interior angles of pentagon is ${540}^o$
$y+y+y+y+y={540}^o$
$5y=540$
$y=\frac{{540}^o}{5}$
$y={108}^o$

Now sum of all exterior angles of polygon is ${360}^o$
$x+x+x+x+x={360}^o$
$5x={360}^o$
$x=\frac{{360}^o}{5}$
$x={72}^o$

So, $\text{difference between interior and exterior angles}=y-x$
$y-x={108}^o-{72}^o$
$y-x={36}^o$

Hence, option $\left(c\right)$ correct.