Question

a) Find the sum of the measures of the angles of a 13-gon.b) Critical Thinking ~ The sum of the measures of the angles of a given polygon is 720. How can you use Sum = ( n - 2 )180 to find the number of sides in the polygon?

Answer 1

A) the geneal formula to find the sum of a figure is:

`(n-2)\cdot180`

where n is the number of sides, so for a 13-gon will be:

`(13-2)\cdot180=11\cdot180=1980`

B) The sum of the angles is 720 so we can replace that in the general formula so:

`(n-2)\cdot180=720`

so we can solve for n to find the number of sides:

`\begin{gathered} (n-2)=(720)/(180) \\ n=4+2 \\ n=6 \end{gathered}`