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

Question

8054 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-21T11:41:59

The polygon is Hexakaidecagon having $16$ sides.

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]