Question

question #5
if ( mangle 4=mangle 8 ) in the drawing, which statement can be concluded?
a ( lperp m )
b ( lparallel m )
c ( mangle 2=mangle 3 )
d ( angle 6 ) and ( angle 7 ) are complementary

Explanation:

Step1: Recall vertical angles and corresponding angles properties

Vertical angles are equal. So \(m\angle4 = m\angle2\) (vertical angles). Given \(m\angle4=m\angle8\), then \(m\angle8 = m\angle2\).

Step2: Use the converse of corresponding angles postulate

If two lines are cut by a transversal and the corresponding angles are equal, then the lines are parallel. Here, \(\angle8\) and \(\angle2\) are corresponding angles. So \(l\parallel m\).

Answer:

B. \(l\parallel m\)