Answer:
The measure of the largest interior angle is [tex]132\°[/tex]
Step-by-step explanation:
we know that
The sum of the interior angles in a polygon is equal to the formula
[tex]S=(n-2)180\°[/tex]
where
n is the number of sides of polygon
In this problem we have a heptagon
so
[tex]n=7\ sides[/tex]
substitute the value in the formula
[tex]S=(7-2)180\°=900\°[/tex]
[tex]S=x+x+(x-2)+(x-2)+(x+2)+(x+2)+(x+4)[/tex]
[tex]900=x+x+(x-2)+(x-2)+(x+2)+(x+2)+(x+4)[/tex]
Solve for x
[tex]900=7x+4[/tex]
[tex]7x=900-4[/tex]
[tex]7x=896[/tex]
[tex]x=128\°[/tex]
Find the measure of the largest interior angle
[tex](x+4)\°=(128\°+4\°)=132\°[/tex]
