Answer:
see the explanation
Step-by-step explanation:
we know that
The sum of the interior angles in any polygon is given by the formula
[tex]S=(n-2)180^o[/tex]
where
n is the number of sides of the polygon
step 1
Find the sum of the interior angles in the given polygon
we have
[tex]n=5\ sides[/tex]
substitute
[tex]S=(5-2)180^o=540^o[/tex]
step 2
Find the value of x
we know that
[tex]-3x+125+(45-x)+(-x+90)+80=540[/tex]
solve for x
[tex]-5x+340=540[/tex]
[tex]-5x=200\\x=-40[/tex]
step 3
Find the measure of each interior angle
substitute the value of x
Angle A
[tex]-3(-40)=120^o[/tex]
Angle B
[tex]80^o[/tex]
Angle C
[tex]-(-40)+90=130^o[/tex]
Angle D
[tex]45-(-40)=85^o[/tex]
Angle E
[tex]125^o[/tex]
