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.
Six angles.
There are 435 angles in the figure because (30/2)(30-1) is equal to 15 * 29 and the answer is 435
An angle is formed by two rays with a common endpoint.
An angle is formed by a point on the end and two rays
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.
Six angles.
There are 435 angles in the figure because (30/2)(30-1) is equal to 15 * 29 and the answer is 435
4
10 rays can meet in 45 vertices. At each such vertex there will be 4 angles which makes 180 angles in all.
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.
3
An angle is formed by two rays with a common endpoint.
21 - including one of 360 degrees.
An angle is formed by a point on the end and two rays
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
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.)