Find the value of $\angle x$ without using trignomoetry

euclidean-geometrygeometry

I found this geometry question in a math video I watched recently.

$$\triangle ABC$$ is an equilateral triangle and point O is a random point taken inside the $$\triangle ABC$$ such that,

$$\angle OAB=x, \angle OBC=42, \angle OCB=54$$

The question is to find the value of $$\angle x$$. The person in the video solved this by using trigonometric ratios and the Ceva's theorem.

The final answer is $$\angle x = 48$$

My approach:

I tried very much time to solve the problem I reflect point O as the line of reflection would be BC and using some algebra by calculating angle BOC nothing wasn't helpful for me to find the value of angle x

But unfortunately I don't like trigonometry and I don't know Ceva's theorem.

So anyone in this community could help me to solve the problem.

Thank you !

Thus we have a proof, using only (?) Euclidean geometry and no trigonometry, that an equilateral triangle can be partitioned into three triangles with angles (6,12,162)°, (18,48,114)°, and (42,54,84)°. Now, if we are requested to find $$x$$ in the picture of the question, when we know that OBC on the left is 42° and OCB on the right is 54°, then previous partition shows that $$x=48°$$.