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Answered

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hello there,

can someone please help me with this question

Hello There Can Someone Please Help Me With This Question class=

Sagot :

Estellia

Answer:

10 sides.

Step-by-step explanation:

Two same interior angles + 72 degrees = 360.

Thus, the interior angle of the polygon is [tex]\frac{360-72}{2} =144[/tex].

The formula to find the interior angle of a polygon is [tex]\frac{180(n-2)}{n}[/tex]

[tex]\frac{180(n-2)}{n} =144[/tex]

Multiply both sides by n:

[tex]\frac{180\left(n-2\right)}{n}n=144n[/tex]

[tex]180\left(n-2\right)=144n[/tex]

Expand:

[tex]180n-360=144n[/tex]

Add 360 to both sides:

[tex]180n-360+360=144n+360[/tex]

[tex]180n=144n+360[/tex]

Subtract 144n from both sides:

[tex]180n-144n=144n+360-144n[/tex]

[tex]36n=360[/tex]

Divide both sides by 36:

[tex]\frac{36n}{36}=\frac{360}{36}[/tex]

[tex]n=10[/tex]

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