Question

given: abcde ≅ jklmn

Explanation:

Step1: Recall property of congruent polygons

Corresponding sides and angles of congruent polygons are equal.

Step2: Find length of JN

Since $ABCDE\cong JKL MN$, side $AE$ corresponds to side $JN$. Given $AE = 22$ ft, so $JN=22$ ft.

Step3: Find length of DC

Side $ML$ corresponds to side $DC$. Given $ML = 17$ ft, so $DC = 17$ ft.

Step4: Find length of KL

Side $BC$ corresponds to side $KL$. Given $BC=12$ ft, so $KL = 12$ ft.

Step5: Find measure of $\angle D$

$\angle D$ corresponds to $\angle M$. Given $m\angle M=158^{\circ}$, so $m\angle D = 158^{\circ}$.

Step6: Find measure of $\angle K$

$\angle K$ corresponds to $\angle B$. Given $m\angle B = 135^{\circ}$, so $m\angle K=135^{\circ}$.

Answer:

JN = 22 ft
DC = 17 ft
KL = 12 ft
m∠D = 158°
m∠K = 135°