1. **Problem statement:** Given lines $k$ and $\ell$ are parallel, and the measure of angle $ABC$ is 19 degrees. 2. **Part a:** Explain why the measure of angle $ECF$ is 19 degrees. - Since $k \parallel \ell$ and $m$ is a transversal, corresponding angles formed by the transversal with the parallel lines are equal. - Angle $ABC$ is formed at the intersection of $\ell$ and $m$ and measures 19 degrees. - Angle $ECF$ is formed at the intersection of $k$ and $m$. - By the Corresponding Angles Postulate, $\angle ABC = \angle ECF = 19^\circ$. - Translating line $\ell$ by moving point $B$ to $C$ aligns the angles, reinforcing that these angles correspond. 3. **Part b:** Find the measure of angle $BCD$. - Angle $BCD$ and angle $ABC$ are alternate interior angles formed by transversal $m$ intersecting parallel lines $k$ and $\ell$. - Alternate interior angles are congruent when lines are parallel. - Therefore, $\angle BCD = \angle ABC = 19^\circ$. **Final answers:** - $\angle ECF = 19^\circ$ - $\angle BCD = 19^\circ$