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]
