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3 years ago

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

Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

6 0

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 :)

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