Question

in exercises 1 and 2, find ( mangle1 ) and ( mangle2 ).
1.

Explanation:

Step1: Use the property of alternate - interior angles

Since the two lines are parallel and cut by a transversal, \(\angle1\) and the \(41^{\circ}\) angle are alternate - interior angles. So \(m\angle1 = 41^{\circ}\).

Step2: Use the property of supplementary angles

\(\angle1\) and \(\angle2\) are supplementary angles (they form a linear pair). So \(m\angle2=180^{\circ}-m\angle1\). Substitute \(m\angle1 = 41^{\circ}\) into the formula: \(m\angle2 = 180^{\circ}-41^{\circ}=139^{\circ}\).

Answer:

\(m\angle1 = 41^{\circ}\), \(m\angle2 = 139^{\circ}\)