$\triangle ABC$ is a triangle with internal point $O$. Find $\angle x$. As title states, the triangle in the following figure has 3 equal sides and some given angles, and the goal is to find the measure of $\angle x$. As always, I'll post my own approach here, please share your own approaches as well!


This'll be my approach. I'll add an explanation below!

Here's how I go about it:
1.) Label the triangle $\triangle ABC$ with the internal point $O$. Rotate $\triangle BOC$ by $180°$ about the line segment $BC$ such that a new triangle $\triangle BDC$ is formed that is congruent to $\triangle BOC$. Connect $A$ with $D$ via $AD$.
2.) Notice that $\angle ABD=60$ and $AB=BD=BO$, this means that $\triangle ABD$ is equilateral, therefore $AB=BO=BD=AD=CD$. This proves that point $D$ is the circumcenter of $\triangle ABC$. Therefore $\angle ACB$ is half of $\angle ADB$. Which means that $x+20=30$, therefore, $x=10$.
