Since lines M and N are parallel, we can use the properties of angles formed by a transversal intersecting parallel lines.
If angle 1 is 135°, then angle 2, which is on the same side of the transversal and corresponds to angle 1, will be its alternate interior angle.
The alternate interior angles theorem states that alternate interior angles are equal when a transversal intersects two parallel lines. Therefore, angle 2 also measures 135°.
So, the measure of angle 2 is 135°.