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:

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