In calculating the slope between (7,3) and (1,2), one student calculated (3-2) divided by (7-1). another student calculated (2-3) divided by (1-7). are they both correct? why?

Both students are correct because if you subtract the numbers from Greatest to Least you will get a positive result. If you subtract from Least to Greatest you will get a negative result, but both the denominator and the numerator will cancel out. Therefore both ways are mathematically correct. As long as your equation is set up as a y-y1 and x-x1 you will be fine. If the equation is set up as x-y or y-x, it will result in the wrong answer.

Add up all the sides

Agc and bgd are vertical angles