Question

what is vy? vy =

Explanation:

Step1: Use the Angle - Angle - Side (AAS) Congruence Theorem

Since \( \angle V W X=\angle V Y X = 90^{\circ}\), \( \angle W X V=\angle Y X V = 35^{\circ}\), and \(XV = XV\) (common side), then \(\triangle V W X\cong\triangle V Y X\) by AAS.

Step2: Set up the equation for the equal - length sides

Because \(\triangle V W X\cong\triangle V Y X\), we have \(VW = VY\). Given \(VW = 5p\) and \(VY=p + 16\), then \(5p=p + 16\).
Subtract \(p\) from both sides: \(5p-p=p + 16-p\), so \(4p=16\).
Divide both sides by \(4\): \(p=\frac{16}{4}=4\).

Step3: Find the length of \(VY\)

Substitute \(p = 4\) into the expression for \(VY\). Since \(VY=p + 16\), then \(VY=4 + 16\).

Answer:

\(20\)