What geometry theorem is used in this figure?

[FactChecker]

You had best get another calculator.

My calculator is fine. If that was a right angle, the length of $x$ would be 12.8062484748657.
(And the angle would not be bisected to give a partitioning of 4 and 6. Although, I didn't calculate what they should be.)

 

[berkeman]

Thread closed temporarily for Moderation...

 

[berkeman]

After some thread cleanup, the thread will remain closed. Thank you everybody for helping the OP with his question.

 

[barryj]

[Mentor Note -- OP has requested that this clarification post be added to the end of this closed thread]

The moderator closed part 1 before I could post the requested theorem. I have attached the figure and a copy of the theorem from a geometry book for those that are interested.