Question

name: date: period: 2.3 parallel lines / transversals thms. app. directions: find the missing angle measures by applying the angle pair relationship theorems we have learned. be sure to show all work and reasoning including all necessary formulas and theorems. 1. given: ( lparallel m ) find: ( angle h ), ( angle p ), ( angle w ), ( angle x ), ( angle z )

Explanation:

Step1: Find \( \angle x \)

Since \( l\parallel m \), \( \angle x \) and \( 57^{\circ} \) are alternate interior angles. So \( \angle x = 57^{\circ} \).

Step2: Find \( \angle w \)

\( \angle w \) and \( 63^{\circ} \) are alternate interior angles. So \( \angle w = 63^{\circ} \).

Step3: Find \( \angle h \)

\( \angle h \), \( 57^{\circ} \) and \( \angle w \) form a straight - line. So \( \angle h=180^{\circ}-57^{\circ}-63^{\circ}=60^{\circ} \).

Step4: Find \( \angle z \)

\( \angle z \) and \( \angle h \) are alternate interior angles. So \( \angle z = 60^{\circ} \).

Step5: Find \( \angle p \)

\( \angle p \) and \( 63^{\circ} \) are same - side interior angles. So \( \angle p = 180^{\circ}-63^{\circ}=117^{\circ} \).

Answer:

\( \angle h = 60^{\circ} \), \( \angle p = 117^{\circ} \), \( \angle w = 63^{\circ} \), \( \angle x = 57^{\circ} \), \( \angle z = 60^{\circ} \)