Its all about Polygons.. Solve it Mentally :)

All sides in a regular polygon are equal $\implies 156^{\circ}$ is the measure of one angle. Let the number of sides of the polygon $= n$ , then from the formula of angle in a regular polygon, we can equate and solve as follows:

$\begin{aligned} 156 &= \frac{(n-2) \cdot 180}{n} \\ 156n &= 180n - 360 \\ -24n&= -360 \\ n&= \boxed{15} \end{aligned}$

Okay, The formula in finding the measure of the whole polygon is n-2(180), So :

N = Number Of Sides

N-2(180) = Measure of the whole polygon

Measurement of the whole polygon/ N = Measure of One Side

Multiply both sides by N you will get:

Measure of the whole polygon = 156n

N-2(180) = 156n

180n - 360 = 156n

180n - 156n = 360 24n = 360 N = 360/24 N = 15

Therefore the polygon has 15 sides..