An equiangular polygon with n sides has \(162\)-degree interior angles. Find the integer n.

Guest Feb 18, 2022

#1**+1 **

The EXterior angles will be 180 - 162 = 18 degrees

EXterior angles sum to 360

360 / 18 = n

ElectricPavlov Feb 18, 2022

#2**+1 **

You could also write it as an equation:

\(n\) = number of sides in the polygon

\(162n=180(n-2)\)

\(162n=180n-360\)

\(0=18n-360\)

\(18n=360\)

\(n = 20\)

So, the polygon has \(\color{brown}\boxed{20}\) sides like Pavlov said.

(His method is the better method tho...)

BuilderBoi Feb 18, 2022