There are 435 angles in the figure because
(30/2)(30-1)
is equal to 15 * 29
and the answer is 435
2 rays
Six angles.
12
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.
136 * * * * * Actually there are 17*16 = 272 angles. Assuming the rays do not meet at 180 degrees, each pair of rays forms two angles: one less than 180 deg and one greater.
2 rays
Six angles.
900
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
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.
2 rays
136 * * * * * Actually there are 17*16 = 272 angles. Assuming the rays do not meet at 180 degrees, each pair of rays forms two angles: one less than 180 deg and one greater.
3