Big Ideas Math - Algebra 1, A Common Core Curriculum

The variable is $x^{\circ}=125^{\circ}$ and the angle measures of the polygon are $125^{\circ}$ and $135^{\circ}$.
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 $135^{\circ}$.