Question

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

Answer 1

Answer:

$x=6$

Step-by-step 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:

$\frac{4x+1}{5}=\frac{15}{3}$

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

$\frac{4x+1}{5}*5=\frac{15}{3}*5$

$4x+1=5*5$

$4x+1=25$

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,

$\frac{4x}{4}=\frac{24}{4}$

$x=6$

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