How many sides does a gon have if the sum of its angles is 1620 degrees?

To find the number of sides of a polygon, we use the theorem on the sum of the angles of a polygon, according to which the sum of the interior angles of an n-gon is: 180 ° * (n – 2).

Since, according to the specification, the sum of the angles of the polygon is 1620 °, we substitute this value into the formula and find n:

180 ° * (n – 2) = 1620 °;

n – 2 = 1620 ° / 180 °;

n – 2 = 9;

n = 9 + 2;

n = 11.

We got that a polygon with the sum of its interior angles equal to 1620 ° is an eleven-gon.

Answer: 11-gon.