SOLUTION: each interior of regular polygon is 90 less than five times the measure of each exterior angle. how many sides does the polygon have?

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Question 326373: each interior of regular polygon is 90 less than five times the measure of each exterior angle. how many sides does the polygon have?
Answer by vksarvepalli(154) About Me  (Show Source):
You can put this solution on YOUR website!
let the value of each interior angle be x
then the value of each exterior angle will be 180-x
now it is given that
each interior angle is 90 less than five times the measure of each exterior angle.

so x=5(180-x)-90
=> x=900-5x-90
=> 6x=900-90
=> x=150-15
=> x=135
now the value of the interior angle of a regular polygon of
n sides is given by
180(n-2)/n degrees
so here 180(n-2)/n = 135
=> 180n-360=135n
=> 45n=360
so n=8
The no. of sides of the polygon = 8
so it is an octagon