Question

Need quick help please?! Using the Angle Bisector Theorem solve for x.
Show all work.

Answer 1

Using the Angle Bisector Theorem solve for x.

The "Angle Bisector" Theorem says that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

As, we see the figure, AD bisects angle A

So, Applying Angle Bisector theorem, we get,

`(AC)/(CD) =(AB)/(BD)`

`(AC=15)/(CD=3) =(AB=(4x+1))/(BD=5)`

`(15)/(3) =(4x+1)/(5)`

15 divide by 3 gives 5

So, we have

5=
`(4x+1)/(5)`

To get rid of fractions let us multiply by 5 on both sides

5*5=
`(5*(4x+1))/(5)`

25=
`(1*(4x+1))/(1)`

25=4x+1

To solve for x, let us subtract 1 from both sides

25-1=4x+1-1

24=4x+0

Or, 4x=24

To solve for x, let us divide by 4 on both sides

`(4)/(4)x=(24)/(4)`

x=6

Answer: x=6

Answer 2

From the angle bisector theorem;
15/3= (4x+1)/5
solving for x;
4x+1 = 25
4x= 24
x= 6