The sum of the measures of the interior angles of a polygon is 720°. What type of polygon is it?

We will use the concept of polygons to solve the question. All interior angles of any regular polygon are equal to each other.

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.

Explanation: 

The sum of interior angles formula for a regular polygon with p sides is given by,

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°.