1. **Problem Statement:** We have two parallel lines $x \parallel y$ and a transversal intersecting them, creating angles $a^\circ$, $b^\circ$, and $c^\circ$. We need to find the value of angle $a$. 2. **Key Concept:** When a transversal crosses two parallel lines, corresponding angles are equal, and alternate interior angles are equal. Also, angles on a straight line sum to $180^\circ$. 3. **Step 1:** Identify relationships. Since $x \parallel y$, angle $b^\circ$ and angle $c^\circ$ are corresponding angles, so $b = c$. 4. **Step 2:** At the intersection with line $x$, angles $a^\circ$ and $b^\circ$ are supplementary because they form a straight line. So, $$a + b = 180$$ 5. **Step 3:** Substitute $b = c$ into the equation: $$a + c = 180$$ 6. **Step 4:** Solve for $a$: $$a = 180 - c$$ **Final answer:** $$\boxed{a = 180 - c}$$