euclidean geometry – How to get the angle in a trapezoid formed by two triangles?

The problem is as follows:

Find the value of angle $angle BCA$ or $x$.

Sketch of the problem

The alternatives given in my book are as follows:

$begin{array}{ll}
1.&30^circ\
2.&20^circ\
3.&10^circ\
4.&40^circ\
end{array}$

The thing here is without any further hints. I’m stuck.

I was only able to spot.

$triangle ABC$ is isosceles,

$triangle DBC$ is isosceles

But I can’t find any other relationship. What else to do?. How to solve this relying only in euclidean geometry postulates?. Can someone help me here?.

Should congruence be used here or what?.

I’m confused please help me. Please include a drawing in your answer as it would help me to spot what to do or if a construction is needed.