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

Guest Jul 18, 2021

#3**+1 **

In order to complete a 360 degree rotation on the outer sides, we simply find the rotation by subtracting 162 from 180, finding the vertical outer angle

180-162=18

18! Great! Now, it takes 360 degrees to complete one full circular rotation, so we take 360 and divide it by 18, which gives us 20, which is the amount of sides, if each side has an exterior vertical angle of 18. We have one angle that connects 2 sides, so

The answer is \(20 sides\)

PBJcatalinasandwich Jul 18, 2021

#7

#8**+3 **

For future reference, the measure of the angles in an equaingular polygon with n sides is \((n-2)\cdot180\over n\).

WhyamIdoingthis Jul 19, 2021