Question

homework 3.2-parallel lines and transversals
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4 of 6 01:56
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 and a transversal are congruent. So $m\angle4 = m\angle5$.

Answer:

$52$