Angle 1 is 45 degrees because it pairs with the 45 degree angle shown. These two angles are congruent due to the alternate interior angle theorem. This only works when lines a and b are parallel.
Angle 2 is 135 degrees because it must add to angle 1 to result in 180 degrees. This is the same side interior angle theorem. Also, note that the original 45 degree angle is adjacent to angle 2, and these two angles form a straight line, so this is another way to see that 45+135 = 180.
