Question

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

Explanation:

Step1: Find \(m\angle2\)

Since \(\angle2\) and the \(75^{\circ}\) angle are vertical angles.
Vertical angles are equal. So \(m\angle2 = 75^{\circ}\)

Step2: Find \(m\angle1\)

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

Answer:

\(m\angle2 = 75\)
\(m\angle1 = 105\)