Question

Two parallel lines are cut by a transversal as shown below.Suppose m<7=59 degrees. Find m<1 and m<4

Answer 1

Notice that angle 3 is vertical angle with angle 1, and since angle 7 is corresponding angle with angle3, we have that angle 1 = angle 7, thus:

`\measuredangle1=59\degree`

next, since angle 1 and angle 4 are supplementary, we have the following equation:

`\begin{gathered} \measuredangle1+\measuredangle4=180 \\ \Rightarrow59+\measuredangle4=180 \\ \Rightarrow\measuredangle4=180-59=121 \\ \end{gathered}`

therefore, angle 4 equals 121 degrees and angle 1 equals 59 degrees