Question

Here are the options, please help!
1.) 32
2.) 18
3.) 1/9
4.) 216

Answer 1

2.) 18

Explanation:

We have been given an image of angle EDG and ray DF bisects our given angle. We are asked to find the value of x.

To solve for the value of x we will use angle-bisector theorem, which states that all point on the angle bisector are equidistant from the sides of the angle.

By angle-bisector theorem length of side EF is equal to GF.

`EF=GF`

`12x=4x+144`

`12x-4x=4x-4x+144`

`8x=144`

`(8x)/(8)=(144)/(8)`

`x=18`

Therefore, the value of x is 18 and 2nd option the correct choice.

Answer 2

Answer
2) 18

Explanation
I believe you want us to help you find the value of x.
From the figure you can see that the 2 triangles are similar. They share one side (the hypotenuse) and the have an angle of 90o.
So, ∆DEF≅∆DGF
Therefore,
EF=GF
4X+144=12X
8X=144
X=18