Question

if \\( \angle w y x \cong \angle w y z \\), \\( w x = 3 s \\), and \\( w z = s + 30 \\), what is the value of \\( s \\)?

Explanation:

Step1: Apply the Angle - Bisector Theorem (HL Congruence for Right Triangles)

Since \( \angle WYX\cong\angle WYZ\), \( \angle WXY = \angle WZY=90^{\circ}\), and \( WY = WY\) (common side), by the Hypotenuse - Leg (HL) congruence criterion for right - triangles, \( \triangle WXY\cong\triangle WZY\).

Step2: Set up the equation based on congruent sides

If \( \triangle WXY\cong\triangle WZY\), then \( WX = WZ\). Given \( WX = 3s\) and \( WZ=s + 30\), we set up the equation \(3s=s + 30\).

Step3: Solve the equation for \(s\)

Subtract \(s\) from both sides of the equation \(3s=s + 30\). We get \(3s−s=s + 30−s\), which simplifies to \(2s=30\).
Divide both sides by 2: \(s=\frac{30}{2}\).

Answer:

\(15\)