Question

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

Explanation:

Step1: Use Hypotenuse - Leg Congruence

Since \(TS = TR = 71\) and \( \angle S=\angle TQR = 90^{\circ}\), by Hypotenuse - Leg (HL) congruence, \(\triangle TSR\cong\triangle TQR\).

Step2: Use Angle Congruence

Corresponding parts of congruent triangles are congruent. So, \(\angle STR=\angle QTR\).

Step3: Use Angle - Sum Property in Right Triangle

In right - triangle \(TQR\), \(\angle QTR = 90^{\circ}-70^{\circ}=20^{\circ}\).

Step4: Calculate \(\angle SRT\)

In right - triangle \(TSR\), \(\angle SRT=90^{\circ}-\angle STR\). Since \(\angle STR = 20^{\circ}\), then \(\angle SRT=70^{\circ}\).

Answer:

\(70\)