Question

what is $m\angle rst$?
(there is a geometric figure with right angles at t and r, a 68° angle at s, and marked congruent segments. the question is to find the measure of $\angle rst$.)
$m\angle rst = \square ^\circ$

Explanation:

Step1: Identify congruent segments

$QT = QR$ (marked with congruence ticks)

Step2: Note right angles

$\angle QTS = \angle QRS = 90^\circ$

Step3: Use HL congruence

$\triangle QTS \cong \triangle QRS$ (shared hypotenuse $QS$, congruent legs $QT=QR$)

Step4: Corresponding angles are equal

$\angle QST = \angle QSR = 68^\circ$

Step5: Calculate $\angle RST$

$m\angle RST = \angle QST + \angle QSR$
$m\angle RST = 68^\circ + 68^\circ$

Answer:

$136^\circ$