# The sum of the angles of a regular n-gon is 1440 degrees. What is the sum of the angles of another regular

**The sum of the angles of a regular n-gon is 1440 degrees. What is the sum of the angles of another regular polygon if it is known that the vertices of the first polygon taken through one serve as the vertices of the second.**

To solve the problem, we use the theorem on the sum of the angles of a convex polygon:

N is a gon, the sum of the angles is:

180 ° * (n – 2).

By the condition of the problem, the sum of the angles of the n-gon is known, we compose the equation:

180 ° * (n – 2) = 1440 °

n – 2 = 8

n = 10 – the number of angles given by the condition of the polygon.

The number of corners of the second polygon is:

10/2 = 5 (taken through one by condition).

Find the sum of the angles of the pentagon:

180 ° * (n – 2) = 180 ° * 3 = 180 ° * (5 – 2) = 540 °.

Answer: the sum of the angles of the second polygon is 540 °.