The problem is as follows:

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

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.**