Answer
$x=118^{\circ}$
Work Step by Step
This implies that the angle opposite to the angle $62^{\circ}$ is also $62^{\circ}$ and the angle opposite to the angle $x^{\circ}$ is also $x^{\circ}$. We know that the sum of the angles is $360^{\circ}$ .
Therefore, we write the equation and then solve for $x$ as: $62^{\circ}+x^{\circ}+62^{\circ}+x^{\circ}=360^{\circ}$
or, $124^{\circ}+2x=360^{\circ}$
or, $2x=236^{\circ} \implies x=118^{\circ}$
