Use a definition, postulate, or theorem to find the value of x in the figure described. ∠abc and ∠cbd are a linear pair. if m∠abc = m∠cbd = (2x − 8)°, find x. select each definition, postulate, or theorem you will use.
a angle addition postulate
b linear pair theorem
c definition of a linear pair
d definition of an angle bisector the solution is x =

Linear Pair Theorem

Step-by-step explanation:

Linear Pair Theorem says that if two angles forjm linear pair then they are supplementary.

Given :  ∠ABC and ∠CBD are a linear pair.

Since linear pair is supplementary.  

And supplementary angles area dded up to 180 degrees.

Then, ∠ABC +∠CBD = 180°  (1)

Also, if m∠ABC = m∠CBD = (2x − 8)°   [given]       (2)

Then, from (1) and (2), we have

Divide both the sides by 4 , we get

Hence, the correct answer is Option (B) "Linear Pair Theorem"

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