Question

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

Answer 1

The angles 1 and 5 have the same measure, since they are corresponding angles.

Then:

`m\angle5=123^(\circ)`

The angles 5 and 6 are supplementary angles, this means that their measures add up to 180°. Then:

`\begin{gathered} m\angle5+m\angle6=180 \\ \Rightarrow123+m\angle6=180 \end{gathered}`

Substract 123 from both sides of the equation:

`\begin{gathered} m\angle6=180-123 \\ =57 \end{gathered}`

Therefore, the measure of the angle 6 is 57°.