1. **Problem Statement:** We are given two parallel lines $l$ and $m$ cut by a transversal, and we need to find the measure of angle $\angle ABC$. 2. **Key Concept:** When two parallel lines are cut by a transversal, alternate interior angles are equal, and corresponding angles are equal. 3. **Given Information:** The angle adjacent to $\angle ABC$ on line $l$ is $132^\circ$. 4. **Step-by-step Solution:** - Since lines $l$ and $m$ are parallel, the angle on line $l$ adjacent to $\angle ABC$ and $\angle ABC$ itself are supplementary (they form a straight line). - Therefore, their measures add up to $180^\circ$. - Using the supplementary angle rule: $$\angle ABC + 132^\circ = 180^\circ$$ - Subtract $132^\circ$ from both sides: $$\angle ABC = 180^\circ - 132^\circ$$ - Simplify: $$\angle ABC = 48^\circ$$ 5. **Final Answer:** $$\boxed{48^\circ}$$