Question

k bisects $overline{jl}$. $kl = 5x$ and $jl = 80$. find $x$ and $jk$.

Explanation:

Step1: Use bisection property

Since K bisects JL, then JK = KL and JL=JK + KL. So JL = 2KL.

Step2: Substitute given values

Given KL = 5x and JL = 80, we have 80=2\times5x.

Step3: Simplify the equation

80 = 10x.

Step4: Solve for x

x=\frac{80}{10}=8.

Step5: Find JK

Since JK = KL and KL = 5x, substituting x = 8, we get JK=5\times8 = 40.

Answer:

x = 8
JK = 40