1. The problem is to find the value of the angle $x$ in a triangle where the other two angles are given as $136^\circ$ and $61^\circ$. 2. Recall that the sum of the interior angles of any triangle is always $180^\circ$. 3. The angle $136^\circ$ is an exterior angle to the triangle, and it forms a linear pair with the adjacent interior angle. The sum of angles in a linear pair is $180^\circ$. 4. Calculate the interior angle adjacent to $136^\circ$: $$180^\circ - 136^\circ = 44^\circ$$ 5. Now, the three interior angles of the triangle are $x$, $61^\circ$, and $44^\circ$. 6. Use the triangle angle sum property: $$x + 61^\circ + 44^\circ = 180^\circ$$ 7. Simplify: $$x + 105^\circ = 180^\circ$$ 8. Solve for $x$: $$x = 180^\circ - 105^\circ = 75^\circ$$ Final answer: $x = 75^\circ$