In a regular polygon each interior angle is 135° greater than each exterior angle. How many sides has the polygon?

1 Answer
Dec 21, 2017

The polygon is Hexakaidecagon having #16# sides.

Explanation:

Exterior angle of regular polygon of #n# sides is #E=360/n#

Interior angle of regular polygon of #n# sides is #I=(180(n-2))/n#

Given condition , # I=E+135 :.(180(n-2))/n=360/n+135# or

#(180(n-2))/n-360/n=135#. Multiplying by #n# on both sides

we get , #180(n-2)-360=135n# or

#180n-360-360=135n or 180n-135n= 720# or

#45n=720 or n = 720/45 or n=16#

The polygon is Hexakaidecagon having #16# sides. [Ans]