Answer:
[tex]5\ sides[/tex]
Step-by-step explanation:
we know that
The formula to calculate the sum of the interior angles in a polygon is equal to
[tex]S=(n-2)180^o[/tex] ----> equation A
where
n is the number of sides of the polygon
In this problem we have that the sum is equal to
[tex]S=2(90^o)+(n-2)120^o[/tex] ---> equation B
Equate equation A and equation B
[tex](n-2)180^o=2(90^o)+(n-2)120^o[/tex]
solve for n
Applying distributive property both sides
[tex]180n-360=180+120n-240[/tex]
Group terms
[tex]180n-120n=180-240+360[/tex]
Combine like terms
[tex]60n=300[/tex]
Divide by 60 both sides
[tex]n=5\ sides[/tex]
