The angle of a regular N-gon is 135 degrees. Find N.

In the initial data for this task, it is reported that the magnitude of each of the angles of this regular N-gon is 135 °, therefore, the sum of all the angles of this polygon should be equal to 135 * N degrees.

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

180 * (N – 2) = 135 * N,

solving which, we get:

180N – 360 = 135N;

180N – 135N = 360;

45N = 360;

N = 360/45 = 8.

Answer: N = 8.