The other same-side interior angle must have a measure of 180 degrees - 77 degrees = 103 degrees.
Alternate interior angles: The alternate interior angles coincide when a transversal crosses parallel lines. This indicates that the measure of angles is the same when they are in the same place on opposing sides of the transversal. Given that one of these angles is given to be 77 degrees, the other two possible internal angles have to be 77 degrees as well.
Corresponding angles: The corresponding angles are congruent when a transversal crosses parallel lines. This indicates that angles have the same measure when they are on the same side of the transversal and at the same position. Consequently, the other two matching angles need to be 77 degrees as well.
Same-side interior angles: The same-side interior angles are supplemental where a transversal crosses parallel lines. This indicates that 180 degrees is the sum of their angles.
Therefore, Since one of these angles measures 77 degrees, the other same-side interior angle must have a measure of 180 degrees - 77 degrees = 103 degrees.