Question

in the diagram shown, $overline{ab}paralleloverline{cd}$. if $mangle7 = 52^{circ}$, then what is the measure of $angle4?$

Explanation:

Step1: Identify angle - pair relationship

$\angle7$ and $\angle5$ are vertical angles. Vertical angles are congruent. So $m\angle5 = m\angle7=52^{\circ}$.

Step2: Use parallel - line property

Since $\overline{AB}\parallel\overline{CD}$, $\angle5$ and $\angle4$ are alternate interior angles. Alternate interior angles formed by parallel lines are congruent. So $m\angle4 = m\angle5$.

Answer:

$52$