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

If m<10=77, m<7=47 and m<16=139, find the measure of the missing angle m-example-1

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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°.

User Lee Jacobs
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