The angle between two adjacent sides of a regular polygon is 160 degrees. Find the number of its sides

Let N denote the number of sides of a given regular polygon.

In the formulation of the condition for this task, it is reported that the angle between two adjacent sides of a regular polygon is 160 °.

Therefore, the sum of all the angles of a given regular polygon must be equal to 160 ° * N.

On the other hand, the sum of the angles of any regular N-gon is 180 ° * (N – 2), therefore, we can compose the following equation:

180 * (N – 2) = 160 * N,

solving which, we get:

180N – 360 = 160N;

180N – 160N = 360;

20N = 360;

N = 360/20 = 36/2 = 18.

Answer: the number of sides is 18.