Question

applying angle pair relationships
what is ( mangle2 )?
what is ( mangle1 )?

Explanation:

Step1: Find \( m\angle2 \)

Since \( \angle2 \) and \( 75^{\circ} \) are corresponding angles (parallel lines \( x \) and \( w \), transversal \( z \)), \( m\angle2 = 75^{\circ} \).

Step2: Find \( m\angle1 \)

\( \angle1 \) and \( \angle2 \) are supplementary (linear - pair). Using the formula \( m\angle1+m\angle2 = 180^{\circ} \). Substitute \( m\angle2 = 75^{\circ} \), then \( m\angle1=180^{\circ}-75^{\circ} \).

Answer:

\( m\angle2 = 75^{\circ} \)
\( m\angle1 = 105^{\circ} \)