Question

$\triangle pqr \cong \triangle mnr$. find x.

Explanation:

Step1: Use congruent triangles property

Corresponding angles of $\triangle PQR \cong \triangle MNR$ are equal, so $\angle Q = \angle N = 35^\circ$.

Step2: Calculate $\angle PRQ$ in $\triangle PQR$

In right triangle $\triangle PQR$, $\angle P=90^\circ$. Sum of angles in a triangle is $180^\circ$, so:
$\angle PRQ = 180^\circ - 90^\circ - 35^\circ = 55^\circ$

Step3: Identify $x$ as $\angle PRQ$

$x$ is the same as $\angle PRQ$.

Answer:

$55$