Hello,
I hope you can help me,
The first attachment gives the problem with the figure. The 2nd attachment gives a clearer drawing of the figure by me drawing it.
In case you can't read the problem, I'll repeat it here:
In the quadrilateral above, AB=AC=AD. If angle BCA = 65, then x=???

The answer is 40, but I can't get it. I know angle BCA=angle ACD=65 degrees and I know that angle ADC=25 degrees. And then for some reason which I do NOT understand, you're supposed to do 65-25=40.Why?
Thank you for your help .I appreciate.

Hi Jeff,

I redrew the diagram and labeled the point P where the line segments AC and BD meet.

I don't see how you know that angle ACD=65 degrees or that angle ADC=25 degrees. I see that

angle BCA = angle CBA = 65 degrees and, since angle BPC is a right angle,
angle CBP = 25 degrees.

My proof hinges on the fact that triangles BAP and PAD are congruent. Can you see why?

Penny