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 ?
Solution
1. Break Down the Problem
We are given that line is parallel to line . This means we can use properties of transversal lines and corresponding angles. We need to find the measure of .
2. Relevant Concepts
Since and the angles and are given, we can apply the concept of supplementary angles and the properties of corresponding angles.
3. Analysis and Detail
- The angles and are connected through line which acts as a transversal.
- We know:
- First, find :
- Since and is a transversal, and are corresponding angles.
- Thus:
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 is confirmed to be .
Final Answer
The measure of is .
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