Question

cf bisects ∠bcd. find m∠fcd if m∠bcf=(x - 6)° and m∠bcd=(x + 35)°. x = 47 m∠fcd = 41

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{CF}$ bisects $\angle BCD$, we know that $m\angle BCF=m\angle FCD$ and $m\angle BCD = 2m\angle BCF$. So, $x + 35=2(x - 6)$.

Step2: Solve the equation for $x$

Expand the right - hand side: $x + 35=2x-12$.
Subtract $x$ from both sides: $35=x - 12$.
Add 12 to both sides: $x=47$.

Step3: Find $m\angle FCD$

Since $m\angle FCD=m\angle BCF=x - 6$, substitute $x = 47$ into the expression. So, $m\angle FCD=47-6=41^{\circ}$.

Answer:

$41^{\circ}$