Question

if $\angle bce \cong \angle dce$, $be = v + 25$, and $de = 2v$, what is the value of $v$?
$v = \square$

Explanation:

Step1: Identify congruent segments

Since $\angle BCE \cong \angle DCE$, and $EB \perp CB$, $ED \perp CD$, the segments $BE$ and $DE$ are congruent (angle bisector theorem for perpendicular segments).

Step2: Set up equation

Set the expressions for $BE$ and $DE$ equal:
$v + 25 = 2v$

Step3: Solve for $v$

Subtract $v$ from both sides:
$25 = 2v - v$
$v = 25$

Answer:

$25$