Question

if ( uv = ux = 41 ), ( mangle uwv = 2p - 10^{circ} ), and ( mangle uwx = p + 6^{circ} ), what is ( mangle uwx )?

( mangle uwx = square^{circ} )

Explanation:

Step1: Use the Angle Bisector Theorem

Since \(UV = UX = 41\) and \(WU\) is the common side, and \(\angle WXV=\angle WVU = 90^{\circ}\), by the Hypotenuse - Leg (HL) congruence criterion, \(\triangle WUX\cong\triangle WUV\). Then \(\angle UWX=\angle UWV\).
So \(2p - 10=p + 6\).

Step2: Solve the equation for \(p\)

Subtract \(p\) from both sides of the equation \(2p - 10=p + 6\):
\(2p-p-10=p - p+ 6\), which gives \(p-10 = 6\).
Add \(10\) to both sides: \(p=6 + 10=16\).

Step3: Find \(m\angle UWX\)

Substitute \(p = 16\) into the formula for \(m\angle UWX\). Since \(m\angle UWX=p + 6\), then \(m\angle UWX=16+6\).

Answer:

\(22\)