Question

find kl. jl = 45, jk = 4x + 2, and kl = 4x + 3

Explanation:

Step1: Use segment - addition postulate

Since $JL = JK+KL$, and $JL = 45$, $JK = 4x + 2$, $KL=4x + 3$. We substitute these values into the equation: $45=(4x + 2)+(4x + 3)$.

Step2: Simplify the right - hand side of the equation

Combine like terms: $45 = 4x+4x + 2 + 3$, so $45=8x + 5$.

Step3: Solve for $x$

Subtract 5 from both sides: $45−5=8x$, which gives $40 = 8x$. Then divide both sides by 8: $x = 5$.

Step4: Find the length of $KL$

Substitute $x = 5$ into the expression for $KL$. Since $KL=4x + 3$, then $KL=4\times5+3$. Calculate $4\times5+3=20 + 3=23$.

Answer:

23