1. **Problem statement:** Find the measures of angles $\angle b$ and $\angle d$ given that lines $m \parallel n$ and the angles $a=60.7^\circ$, $c=119.3^\circ$, and $d=136.9^\circ$ are provided. 2. **Relevant rules:** When two parallel lines are cut by a transversal, corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary (sum to $180^\circ$). 3. **Find $\angle b$:** - Since $a$ and $b$ are corresponding angles (or vertically opposite depending on the figure), and $a=60.7^\circ$, then $\angle b = 60.7^\circ$. 4. **Find $\angle d$:** - Given $\angle d = 136.9^\circ$ from the problem statement, so no calculation needed. 5. **Verification:** - Check if $\angle c$ and $\angle d$ are supplementary (since they appear to be consecutive interior angles): $$119.3^\circ + 136.9^\circ = 256.2^\circ$$ - This sum is not $180^\circ$, so likely $\angle d$ is given directly and no further calculation is needed. **Final answers:** $$\angle b = 60.7^\circ$$ $$\angle d = 136.9^\circ$$