1. **Stating the problem:** We have two parallel lines $\ell_1 \parallel \ell_2$ cut by a transversal, creating several angles including $a$, $b$, $c$, $d$, $e$, $f$, $g$, $h$, $k$, and $m$. Given $m\angle a = 59^\circ$, $m\angle b = 59^\circ$, and $m\angle a = 121^\circ$ (likely a typo, assuming $m\angle m = 121^\circ$), we want to understand the relationships and find missing angle measures. 2. **Relevant formulas and rules:** - When two parallel lines are cut by a transversal, corresponding angles are equal. - Alternate interior angles are equal. - Consecutive interior angles are supplementary (sum to $180^\circ$). 3. **Using the given information:** - Since $m\angle a = 59^\circ$ and $m\angle b = 59^\circ$, and these angles are likely corresponding or alternate interior angles, this confirms the parallelism. - Given $m\angle m = 121^\circ$, angles supplementary to $m$ will be $180^\circ - 121^\circ = 59^\circ$. 4. **Finding other angles:** - Angles $a$, $b$, and those supplementary to $m$ are $59^\circ$. - Angles supplementary to $a$ or $b$ are $180^\circ - 59^\circ = 121^\circ$. 5. **Summary:** - All angles labeled $a$, $b$, $c$, $h$, etc., that correspond or are alternate interior to $a$ and $b$ measure $59^\circ$. - Angles supplementary to these measure $121^\circ$. This matches the given angle measures and the properties of parallel lines cut by a transversal.