Question

what is vx?
v
99
w
6s
y
99
x
s+75
vx = \square

Explanation:

Step1: Identify Congruent Segments

Since \( VW = WX = 99 \) and \( WY \) is perpendicular to \( VX \), by the Perpendicular Bisector Theorem, \( VY = YX \). So \( 6s = s + 75 \).

Step2: Solve for \( s \)

Subtract \( s \) from both sides: \( 6s - s = 75 \) → \( 5s = 75 \). Divide by 5: \( s = \frac{75}{5} = 15 \).

Step3: Find \( VY \) and \( YX \)

Substitute \( s = 15 \) into \( 6s \): \( VY = 6(15) = 90 \). \( YX = s + 75 = 15 + 75 = 90 \).

Step4: Calculate \( VX \)

\( VX = VY + YX = 90 + 90 = 180 \).

Answer:

\( 180 \)