Question

what is ( mangle rst )?
write your answer as an integer or decimal.
( mangle rst = square^circ )

Explanation:

Step1: Identify triangle type & equal sides

$QR$, $QS$, and $QT$ are radii, so $QS = QT$. Thus, $\triangle QST$ is isosceles, so $\angle QST = \angle QTS$.

Step2: Calculate $\angle QST$

Sum of angles in a triangle is $180^\circ$.
$\angle QST = \frac{180^\circ - 76^\circ}{2} = \frac{104^\circ}{2} = 52^\circ$

Step3: Identify $\angle RST$ as $\angle QST$

Point $Q$ lies on $RS$, so $\angle RST = \angle QST$.

Answer:

$52$