Question

these figures are congruent. what is ( mangle f )?

Explanation:

Step1: Match congruent polygon parts

First, identify the corresponding sides of the congruent quadrilaterals:

• $DE = ST = 26$ yd, $DC = RQ = 34$ yd, $CF = QT = 48$ yd, $EF = RS = 26$ yd

So $\angle F$ corresponds to $\angle S$.

Step2: Verify sum of quadrilateral angles

The sum of interior angles of a quadrilateral is $360^\circ$. For quadrilateral $RQTS$, calculate $\angle S$:
$\angle S = 360^\circ - (71^\circ + 57^\circ + 149^\circ)$

Step3: Compute the missing angle

Calculate the value:
$\angle S = 360^\circ - 277^\circ = 83^\circ$
Since $\angle F \cong \angle S$, $m\angle F = 83^\circ$.

Answer:

$83$