Question

How many sides does a regular polygon have if its each interior angle is 144° ? ​

Answer 1

Answer:

10 sides

It's a polygon with 10 sides

Answer 2

Step-by-step explanation:

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.

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