Answer
The measures of the three interior angles are $80{}^\circ ,50{}^\circ ,50{}^\circ $.
Work Step by Step
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 $.
