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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

54.5°
54.5°

109°
109°

71°
71°

35.5°
35.5°
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Answer 1

To find the measure of angle \( m∠RWU \) when given that \( PQ \parallel RS \) and \( m∠PVT = 109^\circ \), we can use the properties of angles formed when parallel lines are cut by a transversal.

1. Corresponding Angles: When a transversal intersects two parallel lines, corresponding angles are equal.
2. Alternate Interior Angles: Alternate interior angles are also equal.
3. consecutive interior angles: Consecutive interior angles are supplementary (they sum up to 180°).

Given that \( m∠PVT = 109° \):

• If angle \( PVT \) and angle \( RWU \) are alternate interior angles, then \( m∠RWU = 109° \).
• However, if they are supplementary (consecutive interior angles), then we can find \( m∠RWU \) as follows:

\[ m∠RWU = 180° - m∠PVT = 180° - 109° = 71°. \]

Based on the information and patterns, the correct answer for \( m∠RWU \) is:

71°

So the answer is:

• 71°