Question

Hello there, can someone please help me with this question

Answer 1

Answer:

10 sides.

Step-by-step explanation:

Two same interior angles + 72 degrees = 360.

Thus, the interior angle of the polygon is $\frac{360-72}{2} =144$.

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

$\frac{180(n-2)}{n} =144$

Multiply both sides by n:

$\frac{180\left(n-2\right)}{n}n=144n$

$180\left(n-2\right)=144n$

Expand:

$180n-360=144n$

Add 360 to both sides:

$180n-360+360=144n+360$

$180n=144n+360$

Subtract 144n from both sides:

$180n-144n=144n+360-144n$

$36n=360$

Divide both sides by 36:

$\frac{36n}{36}=\frac{360}{36}$

$n=10$