Question

what is ( mangle2 )? (square^{circ}) what is ( mangle1 )? (square^{circ})

Explanation:

Step1: Find \(m\angle2\)

Since \(x\parallel w\), \(\angle2\) and \(75^{\circ}\) are alternate - interior angles.
By the Alternate - Interior Angles Theorem, \(m\angle2=75^{\circ}\)

Step2: Find \(m\angle1\)

\(\angle1\) and \(\angle2\) are supplementary (they form a linear pair).
Using the formula \(m\angle1 + m\angle2=180^{\circ}\)
Substitute \(m\angle2 = 75^{\circ}\) into the formula: \(m\angle1=180^{\circ}-75^{\circ}\)
\(m\angle1 = 105^{\circ}\)

Answer:

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