Question

The number of sides of a regular polygon whose each interior angle is of 135° is ______.

Options

• 6

• 7

• 8

• 9

Answer 1

The number of sides of a regular polygon whose each interior angle is of 135° is 8.

Explanation:

We know that, the measures of each exterior angle of a polygon having n sides is given by `360^circ/n`.

∴ The number of sides,

`n = 360^circ/"Exterior angle"`

= `360^circ/(180^circ - 135^circ)`   ...[∵ Exterior angle + Interior angle = 180°]

= `360^circ/45^circ` 

= 8