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?

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) (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
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