Question

line r is parallel to line t. find m∠6. the diagram is not to scale.

Explanation:

Step1: Identify vertical - angle relationship

The angle of 138° and ∠1 are vertical angles. So, $m\angle1 = 138^{\circ}$.

Step2: Use corresponding - angle property

Since line $r$ is parallel to line $t$, ∠1 and ∠2 are corresponding angles. So, $m\angle2=m\angle1 = 138^{\circ}$.

Step3: Identify vertical - angle relationship for ∠6

∠2 and ∠6 are vertical angles. Since vertical angles are congruent, $m\angle6=m\angle2$.

Answer:

138