Question

What is the value of x? Enter your answer in the box. mm

Answer 1

`x=98`

Explanation:

We have been given that diagram of a triangle. We are asked to find the value of the x.

We will use angle bisector theorem to solve for x. Angle bisector theorem states, when a line segment bisects an angle of a triangle, then it divides opposite into segments that are proportional to each other.

We can set a proportion as:

`(VY)/(TV)=(KY)/(TK)`

`(VY)/(57)=(68)/(129.2)`

`(VY)/(57)* 57=(68)/(129.2)* 57`

`VY=30`

Now we will add the lengths of VY and YK to find the value of x.

`x=VY+YK`

`x=30+68`

`x=98`

Therefore, the value of x is 98 mm.