Question

If each interior angle of a regular polygon is 144 degree. Find the number of sides of the polygon.
​

Answer 1

$✔Verified answer</p><p>$

According to question,

Given :

Interior angle =144⁰

Exterior angle =180⁰−144⁰

=36∘

∴no. of sides=360⁰/Exteriorangle∴

360⁰/36⁰=10

Thus , polygon has 10 number of sides

Answer 2

Answer:

                      Here you go mate.

Step-by-step explanation:

Given:

             The polygon is a regular polygon ,

             One of its angle = 144

Formula for sum of all interior angle of a polygon :

            ( n - 2 ) x 180 { where n is number of sides of the given polygon }

As we know it is a regular polygon all angles and sides of this polygon are equal.

A polygon having n sides have n number of angles.

One angle of a polygon    = Sum of all angles

                                              number of angles

One angle of this polygon = ( n - 2 ) x 180  = 144

                                                          n

144n = ( n - 2 ) x 180

144n = 180n - 360

360 = 180n - 144n

360 = 36n

n = 360/36

=10

So required polygon has 10 sides and polygon with 10 sides is DECAGON.

                               ( OR )

Interior angle + Exterior Angle = 180

Exterior Angle = 180 - 144

                        = 36

As we know sum of all Exterior angles = 360 and each exterior angle = 36

No. of sides = 360/36

                    = 10

                                          Answer: Decagon

Hope it was helpful.

Please Rate , Thank , and Mark my answer as the Brainliest if you think I deserve it.