# Question 3ccb5

Mar 31, 2017

$25$

#### Explanation:

Let the size of an exterior angle be ${x}^{\circ}$
Given that the size of the interior angle is ${151.2}^{\circ}$ bigger than its exterior angle
$\implies$ the size of the interior angle $= x + 151.2$

An exterior and interior angle are supplementary angles.

$\implies x + \left(x + 151.2\right) = {180}^{\circ}$
⇒2x=180-151.2#
$\implies x = {14.4}^{\circ}$

The sum of the exterior angles of a polygon is always ${360}^{\circ}$

Number of sides $= \frac{360}{14.4} = 25$