Assuming none of the rays meet at 180 degrees, each pair of rays gives rise to two angles: one less than 180 deg and one greater. There can, therefore, be a maximum of 30*29 = 870 angles.
(There are 435 unique pairs of rays: ab, ac, ad...bc, bd, be, etc.)
Six angles.
An angle is formed by two rays with a common endpoint.
vertical opposite equal angles
Angles in the same plane that have a common vertex and a common side are called adjacent angles. These angles share one side and the vertex where they meet, but they do not overlap. Adjacent angles can be formed by two rays emanating from a common point, and their measures can be added together to find the angle formed by the entire rotation around the vertex.
An angle is formed by two rays with a common endpoint.
Six angles.
3
if the rays have no common points, the answer is zero. if the rays all have the same end point, the answer is 21 -- counting only the acute angles.
An angle is formed by two rays with a common endpoint.
21 - including one of 360 degrees.
4
10 rays can meet in 45 vertices. At each such vertex there will be 4 angles which makes 180 angles in all.
It is 360 degrees.
vertical opposite equal angles
An angle is formed by two rays with a common endpoint.
An angle is formed by two rays with a common endpoint.
Ten.Each angle is determined by two rays, so the answer is equivalent to the number of combinations of 2 out of 5 = 5*4/(2*1) = 10