1. **Problem Statement:** We have two parallel lines cut by a transversal. Given that $m \angle 1 = 76^\circ$, find $m \angle 6$ and $m \angle 8$. 2. **Key Concepts:** When two parallel lines are cut by a transversal, corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary. 3. **Step 1: Identify angle relationships.** - $\angle 1$ and $\angle 5$ are corresponding angles, so $m \angle 5 = 76^\circ$. - $\angle 5$ and $\angle 6$ are adjacent angles on a straight line, so they are supplementary. 4. **Step 2: Calculate $m \angle 6$.** $$ m \angle 5 + m \angle 6 = 180^\circ $$ $$ 76^\circ + m \angle 6 = 180^\circ $$ $$ m \angle 6 = 180^\circ - 76^\circ = 104^\circ $$ 5. **Step 3: Calculate $m \angle 8$.** - $\angle 6$ and $\angle 8$ are vertical angles, so they are equal. $$ m \angle 8 = m \angle 6 = 104^\circ $$ **Final answers:** $$ m \angle 6 = 104^\circ, \quad m \angle 8 = 104^\circ $$