Question

lines ( ell ) and ( m ) are intersected by transversal ( t ) and ( ell parallel m ).
if ( m angle 3 = 126 ^ { circ } ), what is ( m angle 5 )?

Explanation:

Step1: Find \(m\angle4\)

Since \(\angle3\) and \(\angle4\) are supplementary (\(\angle3+\angle4 = 180^{\circ}\)), and \(m\angle3=126^{\circ}\), then \(m\angle4=180^{\circ}- 126^{\circ}=54^{\circ}\).

Step2: Use the property of parallel lines

Because \(\ell\parallel m\) and \(t\) is a transversal, \(\angle4\) and \(\angle5\) are alternate - interior angles. Alternate - interior angles are congruent when two parallel lines are cut by a transversal. So \(m\angle5=m\angle4\).

Answer:

\(54\)