900
There is 1 angle between each pair of rays. So 30 rays equals 30 angles. But, if the angles are likened to the spokes of a bicycle wheel, should the 30 rays not completely fill the circumference of the wheel, the 2 outer rays also form an angle. So the possible total is 31 angles.
There are 435 angles in the figure because (30/2)(30-1) is equal to 15 * 29 and the answer is 435
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.)
2 rays
Six angles.
10 rays can meet in 45 vertices. At each such vertex there will be 4 angles which makes 180 angles in all.
Depends on how many rays you combine but, normally only 1 angle.
12
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.
4
2 rays
A circle is 360 degrees, and to find out how many 30-degree angles fit into it, you divide 360 by 30. This calculation shows that there are 12 angles of 30 degrees in a circle.