In the figure below, 𝐴𝐵― is parallel to 𝐷𝐸―, the measure of ∠𝐴𝐵𝐶 is 49°, and the measure of ∠𝐵𝐶𝐷 is 137°. What is the measure of ∠𝐶𝐷𝐸 ?

1. Break Down the Problem

We are given that line $\overline{AB}$ is parallel to line $\overline{DE}$. This means we can use properties of transversal lines and corresponding angles. We need to find the measure of $\angle CDE$.

2. Relevant Concepts

Since $\overline{AB} \parallel \overline{DE}$ and the angles $\angle ABC$ and $\angle BCD$ are given, we can apply the concept of supplementary angles and the properties of corresponding angles.

3. Analysis and Detail

1. The angles $\angle ABC$ and $\angle BCD$ are connected through line $\overline{BC}$ which acts as a transversal.
2. We know: $\angle ABC = 49^\circ$ $\angle BCD = 137^\circ$
3. First, find $\angle DBC$: $\angle DBC = 180^\circ - \angle ABC = 180^\circ - 49^\circ = 131^\circ.$
4. Since $\overline{AB} \parallel \overline{DE}$ and $\overline{BC}$ is a transversal, $\angle DBC$ and $\angle CDE$ are corresponding angles.
5. Thus: $\angle CDE = \angle DBC = 131^\circ.$

4. Verify and Summarize

• We calculated all the necessary angles accurately and utilized the property of parallel lines effectively through corresponding angles.
• The measure of $\angle CDE$ is confirmed to be $131^\circ$.

Final Answer

The measure of $\angle CDE$ is $131^\circ$.