Question

in the diagram shown, $overline{ab}paralleloverline{cd}$. if $angle7 = 52^{circ}$, then what is the measure of $angle4$?

Explanation:

Step1: Identify vertical - angle relationship

$\angle7$ and $\angle5$ are vertical angles, so $m\angle5=m\angle7 = 52^{\circ}$.

Step2: Identify corresponding - angle relationship

Since $\overline{AB}\parallel\overline{CD}$, $\angle5$ and $\angle1$ are corresponding angles. So $m\angle1=m\angle5 = 52^{\circ}$.

Step3: Identify vertical - angle relationship for $\angle4$

$\angle1$ and $\angle4$ are vertical angles. Since vertical angles are congruent, $m\angle4=m\angle1$.

Answer:

$52^{\circ}$