4
supplimentary angles
If I understand the question: Either pair of opposite angles formed by the intersection of 2 lines.
2 rays
Vertical angles
Six angles.
4
There are 66 angles formed by 12 distinct rays with a common endpoint. The first ray by itself doesn't make an angle, the second ray makes 11 distinct angles, the third ray makes 10, the fourth 9, the fifth - 8, the sixth - 7, the seventh-6, the eighth - 5, the ninth- 4, the tenth - 3, the eleventh - 2, and the twelfth - 1 (it makes an angle with the first ray).
10 rays can meet in 45 vertices. At each such vertex there will be 4 angles which makes 180 angles in all.
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
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
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.)
supplimentary angles