Question

if ( mangle vwy=mangle xwy = 36^{circ}), ( vy = 2p), and ( xy=p + 13), what is ( vy)? ( vy=)

Explanation:

Step1: Use the Angle - Bisector Theorem (HL congruence for right triangles)

Since \(m\angle VWY=m\angle XWY = 36^{\circ}\), \(WY\) is the angle - bisector, and \(\angle V=\angle X = 90^{\circ}\), \(WY = WY\) (common side). By the Hypotenuse - Leg (HL) congruence criterion for right - triangles \(\triangle VWY\cong\triangle XWY\).

Step2: Set up the equation

If \(\triangle VWY\cong\triangle XWY\), then \(VY=XY\). Given \(VY = 2p\) and \(XY=p + 13\), we have the equation \(2p=p + 13\).

Step3: Solve the equation for \(p\)

Subtract \(p\) from both sides of the equation \(2p=p + 13\).
\(2p-p=p + 13-p\)
\(p=13\)

Step4: Find the value of \(VY\)

Since \(VY = 2p\) and \(p = 13\), substitute \(p\) into the formula for \(VY\).
\(VY=2\times13\)

Answer:

\(26\)