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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, RS−→∥PQ−→−
. ∠PVU=4x−7
and ∠TWS=2x+27
. Investigate the patterns of angles created when parallel lines are cut by a transversal to identify the value of x.

(1 point)
Responses

118
118

34
34

61
61

17
17
Remaining Attempts : 1View previous attempt
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Answer 1

To find the value of \( x \) from the equations given:

1. Identify the Angles:

   • \( \angle PVU = 4x - 7 \)
   • \( \angle TWS = 2x + 27 \)

2. Use the Parallel Lines Condition: Since \( RS \parallel PQ \) and these angles are formed by a transversal, we can use the relationship between the angles. Here, \( \angle PVU \) and \( \angle TWS \) could represent corresponding angles or alternate interior angles, which are equal. Thus, we set the angles equal to each other:

   \[ 4x - 7 = 2x + 27 \]

3. Solve for \( x \):

   • Subtract \( 2x \) from both sides:

   \[ 4x - 2x - 7 = 27 \] \[ 2x - 7 = 27 \]

   • Add 7 to both sides:

   \[ 2x = 34 \]

   • Finally, divide both sides by 2:

   \[ x = 17 \]

Therefore, the value of \( x \) is \( 17 \).

Response: 17