Answer
The measures of the three interior angles are $75{}^\circ ,75{}^\circ ,30{}^\circ $.
Work Step by Step
By using angle sum property, the equation is obtained as follows:
$x+2y=180{}^\circ $ (I)
We know that one interior angle is y and one exterior angle is $3x+15$ and both lie on the same line; thus, their sum is $180{}^\circ $. And the equation is obtained as:
$\begin{align}
& 3x+15+y=180{}^\circ \\
& 3x+y=165{}^\circ
\end{align}$ (II)
And to solve these equations, multiply equation (I) by $3$ and subtract equation (II):
$\begin{align}
& 5y=375{}^\circ \\
& y=75{}^\circ
\end{align}$
And to obtain the value of x, substitute the value $y=75{}^\circ $ in either of the equations:
$\begin{align}
& x+2\left( 75 \right)=180{}^\circ \\
& x=30{}^\circ
\end{align}$
Hence, the measures of the interior angles are $75{}^\circ ,75{}^\circ ,30{}^\circ $.
