Polygons

[iron wadi]

alright

there's a formula

for the sum of interior angles

which is 180(n-2) where n is the number of sides

so with a pentagon

theres 5 sides

180(5-2) = 180 x 3 = 540

each interior angle = 540/5 = 108

since there's two pentagons

108 x 2 = 216 degrees

angles around a point add to 360

360 - 216 = 144

so we know this mystery shape has an interior angle of 144

go back to the formula

if 180(n-2) is the sum of angles, then 180(n-2)/n is one interior angle

so we have an equation

180(n-2)/n = 144

180(n-2) = 144n

180n - 360 = 144n

36n - 360 = 0

36n = 360

n = 10 sides!

@brave shore