Answer
$x=67^{\circ}$
Work Step by Step
This implies that the angle opposite to the angle $113^{\circ}$ is also $113^{\circ}$ 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: $113^{\circ}+x^{\circ}+113^{\circ}+x^{\circ}=360^{\circ}$
or, $226^{\circ}+2x=360^{\circ}$
or, $2x=134^{\circ} \implies x=67^{\circ}$
