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

1 Answer
Mar 23, 2018

Please read the explanation.

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^@#

#rArr (n-2) = 4#

Add #color(red)2# to both sides of the equation.

#rArr (n-2)+color(red)2 = 4+color(red)2#

#rArr (n-cancel 2)+color(red)cancel 2 = 4+color(red)2#

#rArr 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:

enter image source here

Hope it helps.