Question

in the diagram below, lines y and z are parallel. the measure of ∠1 is 75°. based on the information in the diagram, what is the measure of ∠5?

Explanation:

Step1: Identify vertical - angle relationship

$\angle1$ and $\angle3$ are vertical angles. Vertical angles are equal. So, $m\angle3 = m\angle1=75^{\circ}$.

Step2: Use corresponding - angle relationship

Since lines $y$ and $z$ are parallel, $\angle3$ and $\angle5$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal. So, $m\angle5=m\angle3$.

Answer:

$75^{\circ}$