Answer
The variable is $x^{\circ}=125^{\circ}$ and the angle measures of the polygon are $125^{\circ}$ and $135^{\circ}$.
Work Step by Step
Sum of angle measures $720^{\circ}$.
From the polygon.
Sum of angle measures
$=120^{\circ}+100^{\circ}+120^{\circ}+120^{\circ}+x^{\circ}+(x+10)^{\circ}$
We can write.
$\Rightarrow 120^{\circ}+100^{\circ}+120^{\circ}+120^{\circ}+x^{\circ}+(x+10)^{\circ}=720^{\circ}$
Simplify.
$\Rightarrow 120^{\circ}+100^{\circ}+120^{\circ}+120^{\circ}+x^{\circ}+x^{\circ}+10^{\circ}=720^{\circ}$
$\Rightarrow 470^{\circ}+2x^{\circ}=720^{\circ}$
Subtract $470^{\circ}$ from each side.
$\Rightarrow 470^{\circ}+2x^{\circ}-470^{\circ}=720^{\circ}-470^{\circ}$
Simplify.
$\Rightarrow 2x^{\circ}=250^{\circ}$
Divide each side by $2$.
$\Rightarrow \frac{2x^{\circ}}{2}=\frac{250^{\circ}}{2}$
Simplify.
$\Rightarrow x^{\circ}=125^{\circ}$
$x+10^{\circ}=125^{\circ}+10^{\circ}=135^{\circ}$
Hence, the variable is $x^{\circ}=125^{\circ}$ and the angle measures of the polygon are $125^{\circ}$ and $135^{\circ}$.
