Question

in exercises 1 and 2,
1.
41°
1
2
2.

Explanation:

Step1: Find \(m\angle1\)

Since the two lines are parallel, \(\angle1\) and the \(41^{\circ}\) angle are alternate - interior angles.
By the Alternate - Interior Angles Theorem, \(m\angle1 = 41^{\circ}\)

Step2: Find \(m\angle2\)

\(\angle1\) and \(\angle2\) are supplementary angles (they form a linear pair).
Using the formula \(m\angle1+m\angle2 = 180^{\circ}\), substitute \(m\angle1 = 41^{\circ}\)
\(41^{\circ}+m\angle2=180^{\circ}\)
\(m\angle2=180^{\circ}- 41^{\circ}\)
\(m\angle2 = 139^{\circ}\)

Answer:

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