In triangle $A B C$, angle $A$ is equal to $40^{\circ}$. The triangle is randomly thrown onto a table.

Find the probability that vertex $A$ will end up east of the other two vertices.
Let the triangle fall such that the traversal from A to B and then to C is counterclockwise. Draw a line through vertex A, running strictly from south to north. The event "Vertex A is east of the other two" occurs if and only if vertices B and C are located in the western half-plane relative to the drawn line. The figure below shows the two extreme positions of the triangle, where vertices B and C are not

![](https://cdn.mathpix.com/cropped/2024_05_08_22585010b2534c7ab9ebg-18.jpg?height=594&width=283&top_left_y=186&top_left_x=885)

In the case of the opposite orientation of the triangle, the probability is obviously the same.

## Answer