Question

how many sides does a regular polygon have if each of its interior angles is 144​

Answer 1

Answer:

10 sides

Step-by-step explanation:

A regular polygon, which has all of its interior angles of 144°; then it has 10 sides.

Answer 2

Answer:

It will be having 10 sides.

Step-by-step 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 =

(

2

N

−

4

)

right angles

∴

144

⋅

N

=

(

2

N

−

4

)

⋅

90

144

N

−

180

N

=

−

360

36

N

=

360

N

=

10

It’s a polygon with 10 sides.