If the interior angle of a regular polygon is 144 then

the exterior angle of the said polygon is 180 - 144 = 36

Using the formula of exterior angle of a polygon = 360/n , where n is the number of sides of polygon

36 = 360/n

36n = 360

n = 360/36

n = 10

The polygon with 10 sides is a decagon

Since it is a regular polygon, all interior angles are equal i.e each interior angle is 144 deg

from formula for total angle A, of a polygon; A=(n-2)*180

where n is the number of sides of a regular polygon

Let's get an expression for A, A=144*n

therefore from the formula

144*n=(n-2)*180

solving for n

144n=180n-360

360=180n-144n

360=36n

n=10

Hence, the polygon is a Decagon

All the angles inside a regular polygon are equal, and the sum of the angles is always equal to: 180(n - 2), where n is the number of sides.

Therefore, the measure of an angle inside a polygon is 180(n-2) / n = 144

180(n - 2) = 144n

36n = 360

n = 10

It's a decagon. Hope I helped!!

The measure of each interior angle of a regular polygon with n sides is: 180(n-2)

--------------

n

so set the formula equal to 144 and multiply by n on both sides.

180(n-2)=144n

Distribute: 180n-360=144n

Put like terms together: 36n=360

Divide by 36: n=10

So Decagon

Decagon

total internal angles

=180*(n-2)

= 180 (10-2)

= 180 (8)

= 1440 degrees

1440/10 angles = 144 degrees

144= (n-2)*180/n

gives n=10