The problem asks us to find the value of angle $x$ in the given diagram. The diagram shows two parallel lines cut by two transversals, forming a triangle. We are given two exterior angles: $61^\circ$ and $136^\circ$.

1. Problem Description

The problem asks us to find the value of angle $x$ in the given diagram. The diagram shows two parallel lines cut by two transversals, forming a triangle. We are given two exterior angles: $61^\circ$ and $136^\circ$.

2. Solution Steps

First, we find the interior angles of the triangle adjacent to the given exterior angles.

Since the sum of an exterior angle and its adjacent interior angle is $180^\circ$, we can find the interior angles.

Interior angle 1: $180^\circ - 61^\circ = 119^\circ$.

Interior angle 2: $180^\circ - 136^\circ = 44^\circ$.

Now, we can find the third interior angle of the triangle using the fact that the sum of the angles in a triangle is $180^\circ$.

Third interior angle: $180^\circ - (119^\circ + 44^\circ) = 180^\circ - 163^\circ = 17^\circ$.

Finally, we can find the angle $x$. Since $x$ and the third interior angle are supplementary, their sum is $180^\circ$.

$x = 180^\circ - 17^\circ = 163^\circ$.

3. Final Answer

The size of angle $x$ is $163^\circ$.