1. **Problem Statement:** Given two parallel lines $p \parallel q$ cut by a transversal, find the value of angle $w$ adjacent to the $101^\circ$ angle on line $q$. 2. **Relevant Rules:** - When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. - Adjacent angles on a straight line sum to $180^\circ$. 3. **Step-by-step Solution:** - Since $w$ and the $101^\circ$ angle are adjacent on line $q$, they form a linear pair. - Therefore, their measures add up to $180^\circ$: $$w + 101 = 180$$ 4. **Isolate $w$:** $$w = 180 - 101$$ 5. **Calculate $w$:** $$w = 79$$ 6. **Explanation of Jacob's Mistake:** Jacob likely assumed that $w$ equals the $101^\circ$ angle because he confused corresponding or alternate interior angles, but $w$ is actually supplementary to $101^\circ$ on the same line. **Final answer:** $$w = 79^\circ$$