Question

If an interior angle of a regular polygon measures 144° how many sides does it have?

Answer 1

It’s a `color(blue)(polygon with 10 sides`

`color(red)(Decagon)`

Explanation:

Exterior angle = 180 - Interior angle = 180 - 144 = 36

Total sum of the exterior angles of a polygon = 360

Therefore no. of sides `N = 360 / 36 = 10`

It’s a decagon.

Aliter :
A polygon with N sides will have the sum of the interior angles = `(2N - 4)` right angles

`:. 144 * N = (2N - 4) * 90`

`144 N - 180 N = -360`

`36 N = 360`

`N = 10`

It’s a polygon with 10 sides.