1. **Problem Statement:** Given two parallel lines $p \parallel q$ cut by a transversal $r$, with $\angle s = 79^\circ$ on line $q$ and $\angle x = 101^\circ$ on line $p$. We need to find the measure of $\angle w$ and identify Jacob's mistake. 2. **Relevant Rules:** - When two parallel lines are cut by a transversal, alternate interior angles are equal. - Adjacent angles on a straight line sum to $180^\circ$. 3. **Step 1: Identify $\angle w$ using $\angle s$** Since $p \parallel q$, $\angle s$ and $\angle w$ are alternate interior angles. Therefore, $$\angle w = \angle s = 79^\circ.$$ 4. **Step 2: Check $\angle x$ and $\angle v$ relationship** $\angle x$ and $\angle v$ are adjacent angles on line $p$ and $r$, so $$\angle x + \angle v = 180^\circ.$$ Given $\angle x = 101^\circ$, then $$\angle v = 180^\circ - 101^\circ = 79^\circ.$$ 5. **Step 3: Confirm $\angle w$ and $\angle v$ relationship** $\angle w$ and $\angle v$ are adjacent angles on the transversal between $p$ and $q$, so $$\angle w + \angle v = 180^\circ.$$ Substitute $\angle v = 79^\circ$: $$\angle w + 79^\circ = 180^\circ,$$ $$\angle w = 180^\circ - 79^\circ = 101^\circ.$$ 6. **Step 4: Resolve the contradiction** From alternate interior angles, $\angle w = 79^\circ$, but from adjacent angles, $\angle w = 101^\circ$. This contradiction means $\angle w$ cannot be both. 7. **Step 5: Identify Jacob's mistake** Jacob likely assumed $\angle w$ equals $\angle x$ (101°) because they appear adjacent or corresponding, but $\angle w$ is actually equal to $\angle s$ (79°) by the alternate interior angle theorem. **Final answer:** $$\boxed{\angle w = 79^\circ}$$ **Jacob's mistake:** He incorrectly equated $\angle w$ to $\angle x$ instead of using the alternate interior angle property with $\angle s$.