Question

which of the following would be true of a regular polygon with an interior angle sum of 360°? select all that apply there are seven sides(n-2)×180°=360any interior angle°=(n-2)×180°/4it is a heptagonal interior angles are 90°n=4

Answer 1

The sum of the interior angles of any polygon is:

$\begin{gathered} \text{sum of interior angles= (N-2)}\cdot180 \\ \text{Where N is the number of sides.} \\ \text{If the sum of interior angles is 360, the number sides is:} \\ 360=(N-2)\cdot180 \\ N-2=\frac{360}{180} \\ N=2+2 \\ N=4 \end{gathered}$

So, N=4 is the correct answer. The option of all interior angles are 90° is NOT correct, because a polygon with 4 sides could be regular and not necesarily is a square,