Question

If the sum of the interior angles of a polygon is 540°, what kind of polygon is it?

Answer 1

$\sf \huge \gg{Pentagon}$

Pentagon's Sum of the interior angles is 540°.

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Answer 2

Answer:

It's a pentagon.

Step-by-step explanation:

The sum of interior angles in an n-gon is (n-2)*180°

Look at this like this - a triangle's sum of angles is 180°

For each additional vertex you can split it from the polygon by cutting out a triangle. You can split a quadrangle into 2 triangles. You can cut a pentagon into a triangle and a quadrangle (or 3 triangles in total). You can split a hexagon into a pentagon and a triangle... So each additional vertex adds 180° of interior angles.

So we solve for n

540° = (n-2)*180°;    divide both sides by 180°

3 = (n - 2) * 1

3 = n - 2

n = 5

So it's a pentagon.