Question

if ∠ced ≅ ∠cef, cd = v + 3, and cf = 4v, what is the value of v?

Explanation:

Step1: Apply angle - bisector theorem

Since $\angle CED\cong\angle CEF$, and $CF\perp EF$, $CD\perp ED$, by the angle - bisector theorem, we know that $CD = CF$.

Step2: Set up the equation

Set $v + 3=4v$.

Step3: Solve the equation for $v$

Subtract $v$ from both sides: $3 = 4v - v$.
Simplify the right - hand side: $3 = 3v$.
Divide both sides by 3: $v = 1$.

Answer:

$1$