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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 ?

Question

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 ?

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Solution

1. Break Down the Problem

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

2. Relevant Concepts

Since ABDE \overline{AB} \parallel \overline{DE} and the angles ABC \angle ABC and BCD \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 ABC \angle ABC and BCD \angle BCD are connected through line BC \overline{BC} which acts as a transversal.
  2. We know: ABC=49 \angle ABC = 49^\circ BCD=137 \angle BCD = 137^\circ
  3. First, find DBC \angle DBC : DBC=180ABC=18049=131. \angle DBC = 180^\circ - \angle ABC = 180^\circ - 49^\circ = 131^\circ.
  4. Since ABDE \overline{AB} \parallel \overline{DE} and BC \overline{BC} is a transversal, DBC \angle DBC and CDE \angle CDE are corresponding angles.
  5. Thus: CDE=DBC=131. \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 CDE \angle CDE is confirmed to be 131 131^\circ .

Final Answer

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

This problem has been solved

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