In the given diagram, we are asked to determine the measures of three angles, with $AB \parallel CD$ (parallel lines). From the image, we see that two angles are already provided:

• $\angle C$ is 37°
• $\angle D$ is 149°

The key concepts involved here are the properties of parallel lines and the angles formed by a transversal. Let's identify the other angles based on these properties:

1. Vertically Opposite Angles:

   • Vertically opposite angles are equal. Since $\angle D = 149^\circ$, its vertically opposite angle (denoted at $\angle B$) will also be 149°.

2. Alternate Interior Angles:

   • Since $AB \parallel CD$ and $BF$ acts as a transversal, $\angle A$ and $\angle C$ are alternate interior angles. Therefore, $\angle A = 37^\circ$.

Thus, the measures of the three angles are:

• $\angle A = 37^\circ$
• $\angle B = 149^\circ$
• $\angle C = 37^\circ$

Would you like further clarification on any step?

Related Questions:

1. What are corresponding angles, and how do they relate to parallel lines?
2. Can you explain how transversal lines create alternate interior angles?
3. How do vertically opposite angles arise, and why are they always equal?
4. What other angle relationships exist when two parallel lines are crossed by a transversal?
5. How would the angle measures change if $AB$ and $CD$ were not parallel?

Tip:

Whenever you see parallel lines cut by a transversal, remember to look for alternate interior, corresponding, and vertically opposite angles to quickly determine unknown angles.