Question

lines l and m are parallel. find m∠3 if m∠5 = 38 and m∠6 = 62.
100
80
38
62

Explanation:

Step1: Find m∠7

Since ∠5, ∠6, ∠7 are on a straight line (supplementary), \( m\angle5 + m\angle6 + m\angle7 = 180^\circ \). Given \( m\angle5 = 38^\circ \), \( m\angle6 = 62^\circ \), so \( m\angle7 = 180 - 38 - 62 = 80^\circ \).

Step2: Use parallel lines property

Lines \( l \) and \( m \) are parallel, so ∠3 and ∠7 are alternate interior angles. Thus, \( m\angle3 = m\angle7 = 80^\circ \).

Answer:

80