Question

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

Answer 1

`x=6`

Explanation:

We have been given a triangle and we are asked to solve for x using angle bisector theorem.

Angle bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side of triangle into segments that are proportional to the other two sides.

Using angle bisector theorem we can set an equation as:

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

Let us solve for x by multiplying both sides of our equation by 5.

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

`4x+1=5*5`

`4x+1=25`

Let us subtract 1 form both sides of our equation.

`4x+1-1=25-1`

`4x=24`

Upon dividing both sides of our equation by 4 we will get,

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

`x=6`

Therefore, the value of x is 6 units.

Answer 2

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