Find the first 4 terms and first and second differences in Tn equal to an2 +bn

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Bra1nPowers

03.05.2021

Mathematics

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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

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Find the first 4 terms and first and second differences in Tn equal to an2 +bn​