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Sum of the angles of a n-sided polygon:
\(\mathsf{S_n=180^\circ\cdot (n-2)}\)
In this question, we have a pentagon, so
\(\mathsf{n=5,}\)
then
\(\mathsf{S_5=180^\circ\cdot (5-2)}\\\\ \mathsf{S_5=180^\circ\cdot 3}\\\\ \begin{array}{lcl}
\!\!\!\mathsf{S_5=540^\circ}&\longleftarrow&\textsf{sum of the measures of the internal}\\
&&\textsf{angles of a pentagon.}
\end{array}\)
Let \(\mathsf{x}\) be the measure of the missing angle. So,
\(\mathsf{85^\circ+110^\circ+135^\circ+95^\circ+x=S_5}\\\\
\mathsf{425^\circ+x=540^\circ}\\\\
\mathsf{x=540^\circ-425^\circ}\\\\
\mathsf{x=115^\circ}\quad\longleftarrow\quad\textsf{measure of the missing angle.}\)
I hope this helps. =)
Tags: sum internal angle missing pentagon polygon plane geometry
