What is the value of x when m<AOB = 6x+5, m<BOC = 4x-2, m<AOC = 8x+21?

I'm working with the Geometry book that says HOLT in red at the top, the rest of the book is green with a lopsided building on it. I'm on Chapter 1, section 3, number 31. We are working with angles and none of the book examples or postulates are helping me. I want to understand how to work this problem out.
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1 Answer

From the naming of the angles it would appear that angle AOC is formed by the joining of two lines OA and OC, and a line OB from the join lies in between OA and OC. This means that AOB+BOC=AOC. That is, 6x+5+4x-2=8x+21. So 2x=18 and x=9. Therefore AOB=59, BOC=34 and AOC=93.

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