Question

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 =

Answer 1

Check; it should either be 3x + 6 or 3x - 6. For example if it's 3x + 6 you'd add all 3 angles to get 180 3x + 6 + 3x - 3 + 3x - 3 = 9x = 180 so divide by 9 and get x = 20

or


x=32

there 2 ways to put it so i make it easy for you to understand it

Answer 2

Answer: Linear Pair Theorem

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

`2x+8+2x+8=180\\\\\Rightarrow\ 4x+16=180\\\\\Rightarrow\ 4x=164`

Divide both the sides by 4 , we get

`x=41`

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