To find the measure of $\angle CDE$, follow these steps:

1. Identify given angles and relationships:

   • Line $l$ is parallel to line $m$, and $\angle CDE$ is an angle formed at the intersection of the transversal and $m$.
   • $\angle BCD$ is 115°, and $\angle ABC$ is 57°.

2. Use the properties of parallel lines and transversals:

   • Since $l \parallel m$, corresponding angles are equal. Therefore, the angle corresponding to $\angle ABC$ at $m$ (below $\angle CDE$) is also $57^\circ$.

3. Find $\angle CDE$:

   • At point $D$, angles form a straight line ($180^\circ$) on the transversal.
   • Thus, $\angle CDE = 180^\circ - 57^\circ = 123^\circ$.

Final Answer:

$\boxed{\angle CDE = 123^\circ}$

Would you like further details or clarification?

Related Questions:

1. Why is the sum of angles on a straight line always $180^\circ$?
2. How do parallel line angle relationships help solve geometric problems?
3. Can you explain alternate interior angles with an example?
4. What would $\angle CDE$ be if $\angle ABC$ were $60^\circ$?
5. How does this problem change if $l$ and $m$ were not parallel?

Tip:

Always look for parallel line properties when transversals are present to simplify angle calculations.