1. **Problem statement:** Find the size of angle $x$ given the angles $134^\circ$ and $63^\circ$ in a zigzag shape formed by two parallel horizontal lines and a diagonal line. 2. **Angle facts used:** - Corresponding angles between parallel lines are equal. - Angles on a straight line sum to $180^\circ$. 3. **Step 1:** Identify that the $134^\circ$ angle and the angle adjacent to $x$ on the top-left are supplementary because they form a straight line. 4. **Step 2:** Calculate the adjacent angle to $x$: $$180^\circ - 134^\circ = 46^\circ$$ 5. **Step 3:** Recognize that angle $x$ and the $63^\circ$ angle are alternate interior angles formed by the diagonal crossing the two parallel lines, so they are equal: $$x = 63^\circ$$ 6. **Final answer:** $$\boxed{63^\circ}$$