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
Since AB is parallel to DE, then the alternate interior angles are equal. Therefore, the measure of ∠BCD is equal to the measure of ∠CDE.
Given that the measure of ∠BCD is 137°, then the measure of ∠CDE is also 137°.
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