The sum of the interior angles of a polygon with n sides is 1980°. Find n.

Xavier Dury asked Aug 17, 2023

320,559 views

11 votes

Xavier Dury asked Aug 17, 2023

2.6k points

Your comment on this question:

Email me at this address if a comment is added after mine:Email me if a comment is added after mine

Privacy: Your email address will only be used for sending these notifications.

Email me at this address if my answer is selected or commented on:Email me if my answer is selected or commented on

Privacy: Your email address will only be used for sending these notifications.

21 votes

We can relate the sum of the interior angles of a polygon S with its number of sides n as:

$S=(n-2)\cdot180$

Then, if S=1980 degrees, we can find n as:

$\begin{gathered} 1980=(n-2)\cdot180 \\ n-2=(1980)/(180) \\ n-2=11 \\ n=11+2 \\ n=13 \end{gathered}$

Answer: the polygon has 13 sides (n=13)

Fez answered Aug 24, 2023

by Fez

3.3k points

Email me at this address if a comment is added after mine:Email me if a comment is added after mine

Privacy: Your email address will only be used for sending these notifications.

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

1.6m questions

2.0m answers