Question

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

Answer 1

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]