If one interior angle of an equiangular n-gon is 172 degrees how many sides does the n-gon have?

Answer 1

If internal angle is 172 deg then external angle is 8 deg
similarly the angle at the centre is 8 deg

number of sides is 360/8 = 45

Answer 2

Well, this is the general formula for finding the measure of each interior angle of an n-gon:
[180*(n-2)]/n=x,
where n is the # of sides and x is the result.
[180*(n-2)]/n=172
172n=180n-360
-8n=-360
8n=360
n=45

So the polygon has 45 sides!

Answer 3

you inscribe your polygone in a circle and draw triangles formed by two rayons and one side
if n is the number of sites, you form n triangles and the sum of their angles is 180*n. From this sum you substract 360° which is the sum of the small angles which are at the summit , the center of the circle in which the triangles are formed
so you have 180*n-360 = 172n
8n = 360
n=45