## Precalculus (6th Edition) Blitzer

The measures of the three interior angles are $80{}^\circ ,50{}^\circ ,50{}^\circ$.
By using the angle sum property, the equation is obtained as follows: $x+2y=180{}^\circ$ (I) Since we know that one interior angle is y and one exterior angle is $2x-30$ and both lie on the same line, their sum is $180{}^\circ$ . The equation is obtained as: \begin{align} & 2x-30+y=180{}^\circ \\ & 2x+y=210{}^\circ \end{align} (II) And to solve these equations, multiply equation (I) by $2$ and subtract equation (2): \begin{align} & 3y=150{}^\circ \\ & y=50{}^\circ \end{align} And to obtain the value of x; put the value $y=50{}^\circ$ in either of the equations: \begin{align} & x+2y=180 \\ & x+2\times 50=180 \\ & x+100=180 \\ & x=80{}^\circ \end{align} Hence, the measures of the interior angles are $80{}^\circ ,50{}^\circ ,50{}^\circ$.