Question

what are the values of w and x?
r
9
s
32°
w
p
q
x
w =
x =

Explanation:

Step1: Identify congruent - sides

Since the two sides of $\triangle RQS$ and $\triangle PQS$ are marked equal, we consider congruence.

Step2: Use congruence property

By Side - Angle - Side (SAS) congruence (if the two pairs of sides are equal and the included angles are equal), we can say $\triangle RQS\cong\triangle PQS$.

Step3: Find the value of $w$

Corresponding sides of congruent triangles are equal. So $w = 9$ as $RS = 9$.

Step4: Find the value of $x$

Corresponding angles of congruent triangles are equal. So $x = 32$ as the corresponding angle to $\angle P$ is $\angle R$ and $\angle P=32^{\circ}$.

Answer:

$w = 9$, $x = 32$