How many angles are formed by 12 distinct rays with a common endpoint?

Answer 1

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).