Question

1. in the diagram below, if ( jl = 10x - 2 ), ( jk = 5x - 8 ), and ( kl = 7x - 12 ), find ( kl ).

Explanation:

Step1: Use segment addition postulate

Since \(JL = JK + KL\), substitute the given expressions:
\(10x - 2=(5x - 8)+(7x - 12)\)

Step2: Simplify the right - hand side

\(10x - 2 = 5x-8 + 7x-12\)
\(10x - 2=12x-(8 + 12)\)
\(10x - 2=12x - 20\)

Step3: Solve for \(x\)

Subtract \(10x\) from both sides:
\(-2=12x-10x - 20\)
\(-2 = 2x-20\)
Add \(20\) to both sides:
\(-2 + 20=2x\)
\(18 = 2x\)
Divide both sides by \(2\):
\(x=\frac{18}{2}=9\)

Step4: Find \(KL\)

Substitute \(x = 9\) into the expression for \(KL\) (\(KL = 7x-12\)):
\(KL=7\times9-12\)
\(KL = 63-12\)
\(KL=51\)

Answer:

\(51\)