Question

1. if line n is the segment bisector of $overline{ce}$, find the measure of $overline{de}$. $de=square$

Explanation:

Step1: Use property of segment bisector

Since line $n$ is the segment bisector of $\overline{CE}$, we have $CD = DE$. So $x + 6=4x - 21$.

Step2: Solve for $x$

Subtract $x$ from both sides: $6 = 3x-21$. Then add 21 to both sides: $27 = 3x$. Divide both sides by 3, we get $x = 9$.

Step3: Find length of $DE$

Substitute $x = 9$ into the expression for $DE$ ($DE=4x - 21$). So $DE=4\times9-21=36 - 21=15$.

Answer:

$15$