Question

Find the number of sides of a regular polygon whose each exterior angle measures 18⁰.​

Answer 1

Given:-

• exterior angle of a regular polygon measures 18⁰.

To Find:-

• Number of sides of a regular polygon.

Solution:-

regular polygon- sided polygon in which the sides are all the same length and are symmetrically placed about a common center.

We know that,

The exterior angle of Any side of the regular polygon is equal to

$\sf \huge exterior \: angle = \frac{360\degree}{side}$

Now,

$= > 18\degree = \frac{360\degree}{side}$

Both side multiplying by side

$= > 18\degree \times side = 360\degree$

$= > side = \frac{360}{18}$

$\sf= > side = 20$

∴the number of sides of a regular polygon whose each exterior angle measures 18⁰ is 20.