3 years ago

1. Name the property the equation illustrates.

Mathematics

1 answer:

8_murik_8 [283]3 years ago

3 0

Answer:

communtative propperty of addition

Step-by-step explanation:

search up what the communitve property is

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The measures of the angles of a convex polygon form an arithmetic sequence. The least measurement in the sequence is 128º. The g

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$\bf \qquad \qquad \textit{sum of a finite arithmetic sequence}\\\\
S_n=\cfrac{n}{2}(a_1+a_n)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\ a_n=n^{th}~value\\
----------\\
\stackrel{least}{a_1}=128\\\\
\stackrel{greatest}{a_n}=172
\end{cases}$

$\bf S_n=\cfrac{n}{2}(128~+~172)\implies S_n=\cfrac{n}{2}(300)\implies S_n=150n
\\\\\\
\textit{but we also know that sum of all interior angles is }180(n-2)
\\\\\\
\stackrel{\textit{sum of the angles}}{S_n}=\stackrel{\textit{sum of the angles}}{180(n-2)}=150n
\\\\\\
180n-360=150n\implies 30n=360\implies n=\cfrac{360}{30}\implies n=12$

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36 even : 12 odd in simplest form

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