1. **State the problem:** We need to find the size of angle $x$ given two other angles: $136^\circ$ and $61^\circ$. 2. **Identify angle relationships:** The angles $x$ and $136^\circ$ are adjacent and form a straight line, so they are supplementary angles. Supplementary angles add up to $180^\circ$. 3. **Write the formula for supplementary angles:** $$x + 136^\circ = 180^\circ$$ 4. **Solve for $x$:** $$x = 180^\circ - 136^\circ$$ $$x = 44^\circ$$ 5. **Check the other angle $61^\circ$:** It is given but not directly needed to find $x$ in this case. 6. **Angle facts used:** - Supplementary angles sum to $180^\circ$. **Final answer:** $$x = 44^\circ$$