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

Two parallel lines are cut by a transversal. What is the measure of <6?-example-1

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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°.

User Nsinvocation
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