Question

if uv = ux = 91, m∠uwv = z + 30°, and m∠uwx = 2z, what is the value of z?
z = \boxed{\circ}

Explanation:

Step1: Use the Angle Bisector Theorem

Since \(UV = UX = 91\) and \(WX\perp UX\), \(WV\perp UV\), then \(WU\) is the angle bisector of \(\angle VWX\). So \(m\angle UWV=m\angle UWX\).

Step2: Set up the equation

We know that \(m\angle UWV = z + 30^{\circ}\) and \(m\angle UWX=2z\). Then \(z + 30=2z\).

Step3: Solve the equation

Subtract \(z\) from both sides of the equation \(z + 30=2z\). We get \(30=2z - z\), so \(z = 30\).

Answer:

\(30\)