Question

Four of the angles of a pentagon measure 85, 110, 135, and 95. Find the measure of the missing angle.

Answer 1

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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