Solve for X

Question

Given:

 

Equilateral Triangle with an exterior angel of (8x+40)

 

I set up the problem to solve for x this way

 

8x+40+20=180

 

My answer was 15 and incorrect. 

 

 

Answer 1

By definition, if the triangle is equilateral, then all sides (as well as all interior angles) are congruent

All interior angles are 60 degrees .... (180/3 = 60)

 

Exterior angles are supplementary to the interior angles.  so the exterior angle is 180 - 60 = 120 degrees

 

   8x + 40 = 120

           8x = 120 - 40

           8x = 80

             x = 10

 

 

 

     

Answer 2

Kim,

 

Well, lemme ask you a question then.

 

You said that you take 8x + 40, and add 20 to it, and you'll get 180.

 

Go ahead and draw the picture of the triangle with the exterior angle.  Depending on what topic you're covering in class right now, there are a couple of ways to go about this:

 

- I totally agree that you should be able to set up an equation where you take 8x + 40, add something to it, and get 180.  The problem is:  what do you add to it?  If two angles that make a straight line add up to 180, then what's the other angle you need to use?  Hint:  It's an equilateral triangle...so, what's the measure of one of the angles inside?

 

- The exterior angle theorem says that an exterior angle (8x + 40) is equal to the sum of the other two angles inside of the triangle.  If you have an equilateral triangle, then every angle inside is the same.  What are each of those angles?  And if you can figure that out, then you can tell me how much two of those angles would add up to.  And if you can figure that out, then you know what 8x + 40 is equal to. 

 

Either of those help?