Question

Oak Street and Elm Street run parallel to each other. When Main street intersects them, it forms interior 6, measuring 70 degrees. What is the measure of 4?

Answer 1

Angle 6 and angle 4 are consecutive interior angles.

As Oak and Elm are parallel, angles 6 and 4 are supplementary and the sum of their measures is 180 degrees.

Then, we can write:

$\begin{gathered} m\angle4+m\angle6=180\degree \\ m\angle4+70\degree=180\degree \\ m\angle4=180\degree-70\degree \\ m\angle4=110\degree \end{gathered}$

Answer: Option D, m<4 = 110 degrees.

Note: if you compare angles, 4 is the corresponding angle to 8 (they have the same measure). In the picture, 6 and 8 are easily seen as supplementary, adding 180 degrees between the two measures.