Answer
$t = 2$
$x = 15$
Work Step by Step
We are given that $\triangle ABC$ is congruent to $\triangle KLM$. We know that corresponding parts of congruent angles are congruent. Therefore, we can deduce that $\overline{AB}$ is congruent to $\overline{KL}$, so let us set those two line segments equal to one another to find the value of $t$:
$AB = KL$
$4 = 2t$
Divide each side by $2$ to solve for $t$:
$t = 2$
According to the triangle sum theorem, we know that the sum of the three interior angles of a triangle equals $180^{\circ}$. If we are already given two of the angles, we can figure out the third angle. If $\triangle ABC$ is congruent to $\triangle KLM$, then $\angle A$ is congruent to $\angle K$, $\angle B$ is congruent to $\angle L$, and $\angle C$ is congruent to $\angle M$. This means that both $\angle A$ and $\angle K$ are $45^{\circ}$, and $\angle B$ and $\angle L$ are $90^{\circ}$. $m \angle C$ is given by the following equation:
$m \angle C = 180 - (45 + 90)$
Evaluate the parentheses first:
$m \angle C = 180 - (135)$
Subtract to find $m \angle C$:
$m \angle C = 45$
Since $\angle C$ and $\angle M$ are congruent, we can set them equal to one another to solve for $x$:
$45 = 3x$
Divide both sides by $3$ to solve for $x$:
$x = 15$
