What is the measure of a triangle if one angle measures 57 degrees?

The inner angles of a triangle will always add up to 180. Assuming that this particular triangle is a right triangle (that is, one of it's angles is 90 degrees), you can find the other angle by subtracting the known angles from 180:

180 - 57 - 90 = 33 degrees

If the triangle is an equilateral or a scalene triangle, the other angles cannot be calculated without additional information.