Question

If m<10=77, m<7=47 and m<16=139, find the measure of the missing angle m<11=?

Answer 1

According to the graph, angle 10 is equal to angle 8 by alternate interior angles.

`m\angle8=m\angle10=77`

Now, we can use the interior angles theorem on the triangle containing 8,7, 11.-

`\begin{gathered} m\angle8+m\angle7+m\angle11=180 \\ 77+47+m\angle11=180 \\ m\angle11=180-77-47 \\ m\angle11=56 \end{gathered}`

Therefore, angle 11 measures 56°.