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disa [49]
3 years ago
10

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 <span>polygonwith10side<span>s
</span></span>

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

Total sum of the exterior angles of a polygon = 360

Therefore no. of sides <span>N=<span>36036</span>=10</span>

It’s a decagon.

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

<span>∴144⋅N=<span>(2N−4)</span>⋅90</span>

<span>144N−180N=−360</span>

<span>36N=360</span>

<span>N=10</span>

It’s a polygon with 10 sides.

i hope u understand :)

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