Given:
Sum of interior angle
To find:
Number of sides of a polygon
Solution:
Using sum of interior angles formula:
[tex]$S=(n-2) \times 180^{\circ}[/tex]
where "S" is the sum of interior angels and "n" is the number of sides of a polygon.
Divide by 180° on both sides.
[tex]$\frac{S}{180^{\circ}}=\frac{(n-2) \times 180^{\circ}}{180^{\circ}}[/tex]
Cancel common factor 180°.
[tex]$\frac{S}{180^{\circ}}=n-2[/tex]
Add 2 on both sides.
[tex]$\frac{S}{180^{\circ}}+2=n-2+2[/tex]
[tex]$\frac{S}{180^{\circ}}+2=n[/tex]
Switch the sides.
[tex]$n=\frac{sum}{180^{\circ}}+2[/tex]
Therefore number of sides of a polygon is [tex]n=\frac{sum}{180^{\circ}}+2[/tex].
