Question

Use a definition, postulate, or theorem to find the value of x in the figure described.

Answer 1

The Definition of Linear Pair states that both ∠ABC and ∠CBD are equal to 180 degrees. In the question, this tells you that 
m∠ABC and m∠CBD = (3x − 6). 
So, you're equation should be (3x - 6) + (3x - 6) = 180. 
You would then solve to get 6x - 12 = 180, 6x = 192, x = 32
x=32, and we used the Linear Pair Theorem (C)