Question

partially correct
your answer is incorrect.

• answer 1: your answer is incorrect.
• answer 3: your answer is incorrect.

consider parallelogram qrst below.
use the information given in the figure to find ( mangle r ), ( mangle rqs ), and ( x ).
(figure of parallelogram qrst with side qt labeled ( 4x ), side rs labeled 8, angle at t labeled ( 71^circ ), angle at s labeled ( 54^circ ), and a triangle qrs inside)
( mangle r = 55^circ )
( mangle rqs = 54^circ )
( x = 27.25 )

Explanation:

Step1: Find $m\angle R$

In a parallelogram, opposite angles are equal, so $m\angle R = m\angle T$.
$m\angle R = 71^\circ$

Step2: Find $m\angle RQS$

In parallelogram $QRST$, $QR \parallel TS$, so alternate interior angles are equal. $\angle RQS = \angle QST$.
$m\angle RQS = 54^\circ$

Step3: Solve for $x$

In parallelogram $QRST$, opposite sides are equal, so $QT = RS$.
$4x = 8$
$x = \frac{8}{4} = 2$

Answer:

$m\angle R = 71^\circ$, $m\angle RQS = 54^\circ$, $x = 2$