Question

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

Explanation:

Step1: Match congruent figure parts

Identify corresponding sides: $BC=KJ=38\ \text{m}$, $DE=LK=20\ \text{m}$, so $\angle D$ corresponds to $\angle K$.

Step2: Find $\angle K$ via quadrilateral sum

Sum of quadrilateral angles is $360^\circ$. Calculate $\angle K$:
$\angle K = 360^\circ - 57^\circ - 154^\circ - 59^\circ$

Step3: Compute the angle value

$\angle K = 360^\circ - (57^\circ+154^\circ+59^\circ) = 360^\circ - 270^\circ = 90^\circ$

Step4: Equate to $\angle D$

Since congruent figures have matching angles, $m\angle D = m\angle K$.

Answer:

$90$