Question

if qr = qt = 97 and m∠qst = 58°, what is m∠qsr?
m∠qsr = °

Explanation:

Step1: Use Hypotenuse - Leg Congruence

Since \(QR = QT = 97\) and \(QS\) is a common hypotenuse (\(QS = QS\)), and \(\angle QTS=\angle QRS = 90^{\circ}\), by Hypotenuse - Leg (HL) congruence, \(\triangle QTS\cong\triangle QRS\).

Step2: Use Congruent Triangles' Angles

Because \(\triangle QTS\cong\triangle QRS\), \(\angle QST=\angle QSR\). Given \(m\angle QST = 58^{\circ}\), so \(m\angle QSR=58^{\circ}\).

Answer:

\(58\)