n a heptagon, the degree measures of the interior angles are $x, ~x, ~x-2, ~x-2,~x + 2, ~x + 2$ and $x + 4$ degrees. What is the degree measure of the largest interior angle?
Accepted Solution
A:
Answer:The measure of the largest interior angle is [tex]132\°[/tex]Step-by-step explanation:we know thatThe sum of the interior angles in a polygon is equal to the formula[tex]S=(n-2)180\°[/tex]wheren is the number of sides of polygonIn this problem we have a heptagonso[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]