Question

if (mangle qsr = mangle qst = 56^{circ}) and (qr = 15), what is (qt)?

Explanation:

Step1: Identify congruent triangles

In right - triangles $\triangle QSR$ and $\triangle QST$, $\angle QSR=\angle QST = 56^{\circ}$, $\angle SRQ=\angle STQ = 90^{\circ}$, and $QS$ is common. By the Angle - Angle - Side (AAS) congruence criterion, $\triangle QSR\cong\triangle QST$.

Step2: Use congruent - triangle property

Since $\triangle QSR\cong\triangle QST$, corresponding sides are equal. Given $QR = 15$, and $QR$ and $QT$ are corresponding sides of congruent triangles. So $QT=QR$.

Answer:

$15$