from a handpicked tutor in LIVE 1-to-1 classes
The sum of the measures of the interior angles of a polygon is 720°. What type of polygon is it?
Answer: The polygon having the sum of interior angles as 720° is Hexagon.
Let’s solve this question by using the sum of interior angles formula.
Sum of interior angles of a polygon = 180(p – 2).
720° = 180(p – 2) [Since, sum = 720° (Given)]
⇒ 720° / 180º = (p – 2)
⇒ 4 = (p – 2)
⇒ p = 4 + 2
⇒ p = 6
Thus, we see that the polygon has 6 sides.
We know that the polygon that has 6 sides is called a hexagon.
The figure of a regular hexagon is shown below:
Thus, it is a regular hexagon that has the sum of the measure of the interior angles as 720°.