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Each exterior angle of a polygon has a measure of 400. how many sides does the regular polygon have??
A.8
B.9
C.10
D.11

Sagot :

JESUSAGIGANTONEGO

Answer:

Each exterior angle of a polygon has a measure of 400. how many sides does the regular polygon have?

B. 9

Answer:

B. 9

Solution:

The exterior angle is 40°, right? Not 400°

First, find the interior angle

θ = 180 - 40 = 140°

The formula for the interior angle of a polygon with n-side is

θ = [tex]\frac{180(n-2)}{n}[/tex]

[tex]140=\frac{180(n-2)}{n}[/tex]

[tex]140n=180n-360[/tex]

[tex]180n-140n=360[/tex]

[tex]40n=360[/tex]

[tex]n=\frac{360}{40}=9[/tex]

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