Question

If an interior angle of a regular polygon measures 144°, how many sides does the polygon have?

Answer 1

It’s a polygonwith10sides

Exterior angle = 180 - Interior angle = 180 - 144 = 36

Total sum of the exterior angles of a polygon = 360

Therefore no. of sides N=36036=10

It’s a decagon.

Aliter :
A polygon with N sides will have the sum of the interior angles = (2N−4) right angles

∴144⋅N=(2N−4)⋅90

144N−180N=−360

36N=360

N=10

It’s a polygon with 10 sides.

i hope u understand :)