Use the image to answer the question.

Question

The intersection of Atlantic Street and Ocean Avenue is labeled from top left as a, top right as 130 degrees, bottom right as c, and bottom left as b. The intersection of Pacific Street and Ocean Avenue is labeled from top left as d, top right as e, bottom right as g, and bottom left as f. The streets and avenue are made up of solid lines containing dashed lines at their centers.

In the diagram, given PQ−→−∥RS−→, m∠PVT=109°. Investigate the patterns of angles created when parallel lines are cut by a transversal to identify m∠RWU.

(1 point)
Responses

109°
109°

54.5°
54.5°

35.5°
35.5°

71°
71°

Answer 1

To find the measure of angle \( m∠RWU \), we need to apply the properties of angles created when a transversal crosses parallel lines.

Given that \( PQ \parallel RS \) and \( m∠PVT = 109° \), we can analyze the transversal that intersects these parallel lines.

According to the properties of parallel lines cut by a transversal:

1. Corresponding Angles: Angles located in the same position at each intersection are equal.
2. Alternate Interior Angles: Angles located on opposite sides of the transversal but inside the parallel lines are equal.
3. Consecutive Interior Angles: Angles located on the same side of the transversal (but inside the parallel lines) are supplementary, meaning they add up to 180°.

In this case, \( m∠PVT \) is given as \( 109° \).

Let's use the Corresponding Angles property:

• If \( m∠PVT = 109° \), then the corresponding angle \( m∠RWU \) (assuming that \( RW \) is parallel to \( PQ \) and \( RS \)) will be equal to \( 109°\).

Therefore, the answer is:

109°.