Question

Look at the photo in the link below.
http://i43.tinypic.com/2rqbr6p.png
Find the value of x.

A. 9
B. 18
C. 45
D. 90

Answer 1

Theres a few things you need to know here.
1. The angles must sum to 360 degrees
2. Opposite angles must be equal

Answer 2

So would I turn it into a problem that would require you to combine like terms and such? Having it equal to 360?

Answer 3

Right! You will need at least two equations here because you have two variables here, x and y, but you ultimately want to find the solution for x.

Answer 4

Similarly, you could use the fact that two adjacent angles must sum to 180 degrees, because together they form a straight line.

Answer 5

So I would do 4x + 2y - x = 180 ?

Answer 6

Not quite! But close, 4x and (2y-x) are opposite angles so they must be equal, 4x and (2y+x) are adjacent so they must be equal!
so..

\[4x = 2y -x\]
and\[4x + 2y + x = 180\]

Answer 7

So how exactly would I get rid of "y" ? I know "x" has to be by itself.

Answer 8

Solve the top equation in terms of x.... by that I mean, add over that -x so it looks like

Answer 9

\[5x = 2y \rightarrow y= 5x/2\]
Now plug in this value of y in the lower equation and solve for x

Answer 10

I'm a bit confused at the answer that I had gotten, I think I may have done this problem completely wrong. It's been awhile since I've done this type of geometry. So I divide the 5x by 2? and if so, I've gotten 2.5

Answer 11

Well y= 2.5x, now you plug in y into that lower equation...
\[4x + 2y + x = 180\]\[5x + 2(\frac{ 5x }{ 2 }) = 180\] \[5x + 5x = 180\] \[10x = 180\] \[x = \frac{ 180 }{ 10 } = 18\]

Answer 12

Oooh okay I think I get it, thank you very much I appreciate it. :)

Answer 13

You're welcome!