The sum of the 80 and 55 degree angles and the unknown angle x must be 180 degrees. Thus, x + 80 + 55 = 180, or x + 155 = 180, or x = 25.
x is 25 degrees.
This is based upon the "corresponding angles" principle. Lines AB and CD are parallel and are intersected by the longer diagonal line if we extend this line past the 80 and 55 degree angles.
