Question

What is the length of AB?

Answer 1

Thanks for your question!

Because the angles are the same, the sides are the same.
So:

6x = 3x + 9
3x = 9
x = 3

But this problem isn't over yet. We need to find AB not x.

6(3) = 18

Hope this helps!

Answer 2

As you can see from the diagram, this is an isosceles triangle (triangle where 2 sides are equal and angles opposite are also equal).

Since there are two 65 degree angles, the sides opposite them are also equal. So we can write:

`6x=3x+9`

Solving for x:

`6x=3x+9\\6x-3x=9\\3x=9\\x=(9)/(3)\\x=3`

Now, we want to know side length of AB, which is 6x. Plugging in x = 3 into that, we get:

`AB=6(3)\\AB=18`

Answer choice D is right.

ANSWER: D