Question

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

Explanation:

Step1: Find \(m\angle2\)

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

Step2: Find \(m\angle1\)

\(\angle1\) and \(\angle2\) are supplementary angles (they form a linear - pair). Using the formula \(m\angle1+m\angle2 = 180^{\circ}\). Substitute \(m\angle2 = 75^{\circ}\) into the formula: \(m\angle1=180^{\circ}-m\angle2\)

$$m\angle1 = 180^{\circ}-75^{\circ}=105^{\circ}$$

Answer:

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