Answer
$x=85$
Work Step by Step
The sum of the four interior angles of a quadrilateral is $360^\circ$.
Thus, the equation needed to find the value of. $x$ is:
$\begin{align*}
x^\circ+150^\circ+77^\circ+48^\circ&=360^\circ\\
x^\circ+275^\circ&=360^\circ\end{align*}$
Solve the equation by subtracting $275^\circ$ from each side:
$\begin{align*}
x^\circ+275^\circ-275^\circ&=360^\circ-275^\circ\\
x^\circ&=85^\circ\\
x&=85
\end{align*}$
The angle is acute and close to $90$ degrees and the value of $x$ is $85$ so the answer is reasonable.
