Question

what is ( mangle srt )?
( mangle srt=square^{circ} )

Explanation:

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

Since \(TS = TQ = 96\) and \(TR\) is common, and \(\angle RST=\angle RQT = 90^{\circ}\), by the Hypotenuse - Leg (HL) congruence criterion for right - triangles, \(\triangle RST\cong\triangle RQT\). So, \(u=2u - 28^{\circ}\).

Step2: Solve the equation for \(u\)

Subtract \(u\) from both sides of the equation \(u=2u - 28^{\circ}\).
We get \(0=2u - u-28^{\circ}\), which simplifies to \(u = 28^{\circ}\).

Step3: Find \(m\angle SRT\)

\(m\angle SRT=u\).

Answer:

\(28\)