# If the sum of the interior angles of a polygon is 720°, what type of polygon is it?

Mar 23, 2018

#### Explanation:

Given:

Sum of the interior angles of a polygon is: color(blue)(720^@

The relationship between the number of sides of a polygon and the sum of interior angles is color(blue)(180^@*(n-2),

where color(blue)(n is the number of sides of the polygon.

Hence, we have

color(blue)(180^@*(n-2)=720^@

Divide both sides of the equation by color(red)(180^@

color(blue)[[180^@*(n-2)]/color(red)(180^@]=720^@/color(red)(180^@

color(blue)[[cancel 180^@*(n-2)]/color(red)(cancel 180^@]=720^@/color(red)(180^@

$\Rightarrow \left(n - 2\right) = 4$

Add $\textcolor{red}{2}$ to both sides of the equation.

$\Rightarrow \left(n - 2\right) + \textcolor{red}{2} = 4 + \textcolor{red}{2}$

$\Rightarrow \left(n - \cancel{2}\right) + \textcolor{red}{\cancel{2}} = 4 + \textcolor{red}{2}$

$\Rightarrow n = 6$

Hence, the required polygon must have 6 sides.

A Hexagon is a six-sided polygon.

Hence, the type of polygon required is a Hexagon.

If you are interested, you can find an image of a regular hexagon below: Hope it helps.