1. **State the problem:** We have two congruent trapezoids ABCD and JKLM. Given angles and side lengths in ABCD, find the measure of angle $\angle L$ and the length $JK$ in trapezoid JKLM. 2. **Recall properties of congruent figures:** Congruent polygons have corresponding angles equal and corresponding sides equal in length. 3. **Identify corresponding parts:** Since ABCD $\cong$ JKLM, vertex A corresponds to J, B to K, C to L, and D to M (both named clockwise). 4. **Given data in ABCD:** - $AB = 4$ in - $DC = 8$ in - $\angle D = 40^\circ$ - $\angle C = 55^\circ$ 5. **Find $\angle L$:** Since $\angle L$ corresponds to $\angle C$, we have $$\angle L = \angle C = 55^\circ.$$ 6. **Find $JK$:** Side $JK$ corresponds to side $AB$, so $$JK = AB = 4 \text{ in}.$$ **Final answers:** $$\boxed{\angle L = 55^\circ}$$ $$\boxed{JK = 4 \text{ in}}$$