Question

Two parallel lines are cut by a transversal. What is the measure of angle 6?

Answer 1

`\huge\boxed{\textsf{D.}\ 57^\circ}`

We know that angles 1 and 2 are supplementary angles that add up to 180 degrees.

Solve for angle 2:

`\begin{aligned}\angle1+\angle2&=180^\circ\\123^\circ+\angle2&=180^\circ\\123^\circ-123^\circ+\angle2&=180^\circ-123^\circ\\\angle2&=57^\circ\end{aligned}`

We also know that angles 2 and 6 are corresponding angles, so they are equal to each other. This means that angle 6 is also 57 degrees.

For more information on this topic, search the Internet. There are many great resources on transversal lines and angles out there that expand on the few details I shared here.