Question

Еhere are n unparallel lines in pairs on a plane. Prove that the angle between two of them is not more then (180°/n).

Answer 1

Let's take a random point on plane and draw lines through it which will be parallel to given lines. The drawn lines will divide a plane into 2n angles which in a sum give 360°. That is why one of those angles do not exceed (180°/n).