The diagram shows that $x^\circ$ is an interior angle of a triangle, and it's formed by two intersecting lines. The given exterior angle is $101^\circ$ and the interior angle opposite to it is $51^\circ$.

The exterior angle theorem states that the exterior angle is equal to the sum of the two opposite interior angles. Therefore:

$x + 51 = 101$

Solving for $x$:

$x = 101 - 51$ $x = 50$

So, $x = 50^\circ$.