The problem states that Susan is trying to find angle $b$. She first finds angle $a$ and then finds angle $b$ from angle $a$. We need to determine which angle facts she uses to find angle $a$ and angle $b$.

1. Problem Description

The problem states that Susan is trying to find angle $b$. She first finds angle $a$ and then finds angle $b$ from angle $a$. We need to determine which angle facts she uses to find angle $a$ and angle $b$.

2. Solution Steps

a) Finding angle $a$:

The $139^{\circ}$ angle and the angle adjacent to $a$ form a straight line.

Angles on a straight line add up to $180^{\circ}$.

So, $139^{\circ} + \text{adjacent angle to } a = 180^{\circ}$.

Therefore, the adjacent angle to $a$ is $180^{\circ} - 139^{\circ} = 41^{\circ}$.

Since angle $a$ and the $41^{\circ}$ angle are corresponding angles formed by parallel lines and a transversal, they are equal.

Thus, $a = 41^{\circ}$.

The angle fact used to find angle $a$ is "corresponding angles are equal".

b) Finding angle $b$:

Angle $a$ and angle $b$ are alternate interior angles formed by parallel lines and a transversal.

Since alternate interior angles are equal, $a = b$.

Therefore, $b = 41^{\circ}$.

The angle fact used to find angle $b$ is "alternate interior angles are equal".

3. Final Answer

a) The angle fact she uses to find angle $a$ is "corresponding angles are equal".

b) The angle fact she then uses to find angle $b$ is "alternate interior angles are equal".