The figure to the right shows two parallel lines intersected by more than one transversal. Let $x=45^{\circ}$. Find the measure of angles 1,2 , and 3 . \[ m \angle 1= \]

Step 1 ：The problem involves the concept of parallel lines and transversals. When a transversal intersects parallel lines, alternate interior angles are congruent. This means that if we know the measure of one angle, we can find the measure of the alternate interior angle. In this case, we know that \(x=45^{\circ}\), so the measure of angle 1, which is an alternate interior angle to x, is also \(45^{\circ}\).

Step 2 ：Final Answer: The measure of angle 1 is \(\boxed{45^{\circ}}\).