Question

find ( mangle1 ) and ( mangle2 ). tell which theorem can be used.

( mangle1=) by the

( mangle2=) by the

Explanation:

Step1: Find \(m\angle1\)

Since the two lines are parallel and the transversal intersects them, \(\angle1\) and the \(117^{\circ}\) angle are congruent. By the Alternate Interior Angles Theorem, \(m\angle1 = 117^{\circ}\).

Step2: Find \(m\angle2\)

\(\angle2\) and the \(117^{\circ}\) angle are congruent. By the Corresponding Angles Theorem, \(m\angle2=117^{\circ}\).

Answer:

\(m\angle1 = 117^{\circ}\) by the Alternate Interior Angles Theorem.
\(m\angle2 = 117^{\circ}\) by the Corresponding Angles Theorem.