Given: Angle 1 = 128 degrees, Angle 2 = 37 degrees, line a is parallel to line b. Find: Angle 3.

Solution:

We are given two parallel lines \( a \) and \( b \), and a transversal line.

Angle 1 and the angle adjacent to Angle 3 on line \( a \) are consecutive interior angles. Consecutive interior angles are supplementary, meaning they add up to 180 degrees.

Let the angle adjacent to Angle 3 on line \( a \) be \( \alpha \).

\( \angle 1 + \alpha = 180^{\circ} \)

\( 128^{\circ} + \alpha = 180^{\circ} \)

\( \alpha = 180^{\circ} - 128^{\circ} \)

\( \alpha = 52^{\circ} \)

Angle 3 and \( \alpha \) are alternate interior angles. Alternate interior angles are equal when lines are parallel.

\( \angle 3 = \alpha \)

\( \angle 3 = 52^{\circ} \)

Note: Angle 2 is not needed to solve for Angle 3 in this configuration.

Answer: \( \angle 3 = 52^{\circ} \)