Proofs About Angles Quick Check

Question

1 of 51 of 5 Items
Question
Use the image to answer the 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

71°
71°

109°
109°

35.5°
35.5°

54.5°

Answer 1

To solve this problem, we need to apply the properties of angles formed when parallel lines are cut by a transversal.

Given that \( PQ \parallel RS \) and \( m\angle PVT = 109^\circ \), we can analyze the relationships between the angles:

1. \( m\angle PVT \) (which is given as \( 109^\circ \)) is an exterior angle at the intersection with a transversal.
2. When parallel lines are cut by a transversal, the corresponding angles are equal, and the alternate interior angles are also equal.

Using these properties, angle \( RWU \) would be the angle that is in a corresponding or alternate position relative to angle \( PVT \):

• Since \( m\angle PVT + m\angle RWU = 180^\circ \) (because they are consecutive interior angles), we can determine \( m\angle RWU \) as follows:

\[ m\angle RWU = 180^\circ - m\angle PVT = 180^\circ - 109^\circ = 71^\circ \]

Therefore, the measure of angle \( RWU \) is \( 71^\circ \).

The answer is 71°.