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Thank you in advance!

 Jan 25, 2021
 #1
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Angle CAD can be equal to angle CBE.  If angles CAD and CBE are not equal, then we can choose a point A' on AD so that angle CA'D is equal to CBE.  So we can move point A to A', and then angles CAD and CBE will be equal.

 Jan 25, 2021
 #2
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Nice answer guest, but I don't think it's correct. Here's why:

Since AD is parallel to BE, Angle BEC = Angle ADC, and therefore, in order for Angle CAD to equal angle CBE, triangles BEC and ADC must be similar to each other. That can only happen if angle BCE = angle ACD, and that can only happen if A is on BC. Since that isn't allowed, angle CAD cannot be equal to angle CBE.

 Jan 26, 2021

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