if the sides of a rectangle triangle measure 6 and 8 cm, what is the measure of the the angles of the triangle?

By rectangle triangle I assume that you mean a right angled triangle.

and that you have the 2 sides that are at right angles to one another.

The Hypoteunuse will be 10 cm 

Anyway here is your triangle.     atan is the same as inverse tan which is  $$tan^{-1}$$