Question

In the figure line l1 is parallel to line l2 if the measure of 3=39 what is the measure of 6 and why

Answer 1

`m\angle 6=39^o` by alternate interior angles

Explanation:

see the attached figure to better understand the problem

we know that

Alternate interior angles are formed when a transversal (in this problem line T) passes through two lines (line L1 and line L2) . The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. When the lines are parallel, the alternate interior angles are congruent.

so

`m\angle 6=m\angle 3` ----> by alternate interior angles

`m\angle 5=m\angle 4` ----> by alternate interior angles

we have that

`m\angle 3=39^o`

therefore

`m\angle 6=39^o`