Question

mangle1=\boxed{117^{circ}} by the \boxed{alternate interior angles theorem} mangle2=\boxed{117^{circ}} by the \boxed{vertical angles congruence theorem} 63^{circ} 117^{circ} alternate exterior angles theorem consecutive interior angles theorem alternate interior angles theorem vertical angles congruence theorem

Explanation:

Step1: Find \(m\angle1\)

By the Alternate Interior Angles Theorem, \(m\angle1 = 117^{\circ}\)

Step2: Find \(m\angle2\)

Since \(\angle1\) and \(\angle2\) are vertical angles, by the Vertical Angles Congruence Theorem, \(m\angle2=m\angle1 = 117^{\circ}\)

Answer:

\(m\angle1 = 117^{\circ}\) (by Alternate Interior Angles Theorem), \(m\angle2 = 117^{\circ}\) (by Vertical Angles Congruence Theorem)