Answer
$110^{\circ},50^{\circ}$ and $20^{\circ}$
Work Step by Step
Sum of angle measures is $180^{\circ}$.
Write the equation.
$\Rightarrow 110^{\circ}+5x^{\circ}+2x^{\circ}=180^{\circ}$
Combine like terms.
$\Rightarrow 110^{\circ}+7x^{\circ}=180^{\circ}$
Subtract $110^{\circ}$ from each side.
$\Rightarrow 110^{\circ}+7x^{\circ}-110^{\circ}=180^{\circ}-110^{\circ}$
Simplify.
$\Rightarrow 7x^{\circ}=70^{\circ}$
Divide each side by $7$.
$\Rightarrow \frac{7x^{\circ}}{7}=\frac{70^{\circ}}{7}$
Simplify.
$\Rightarrow x^{\circ}=10^{\circ}$
Multiply each side by $5$.
$\Rightarrow 5x^{\circ}=50^{\circ}$
Multiply each side by $2$.
$\Rightarrow 2x^{\circ}=20^{\circ}$
Hence, the angle measures of the polygon are $110^{\circ},50^{\circ}$ and $20^{\circ}$
