Question

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

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{CF}$ bisects $\angle BCD$, then $m\angle BCF=\frac{1}{2}m\angle BCD$. So we have the equation $(x - 6)=\frac{1}{2}(x + 35)$.

Step2: Solve the equation for $x$

Multiply both sides of the equation by 2 to get $2(x - 6)=x + 35$. Expand the left - hand side: $2x-12=x + 35$. Subtract $x$ from both sides: $2x-x-12=x - x+35$, which simplifies to $x-12 = 35$. Then add 12 to both sides: $x=35 + 12=47$.

Step3: Find $m\angle FCD$

Since $m\angle FCD=m\angle BCF$ and $m\angle BCF=(x - 6)^{\circ}$, substitute $x = 47$ into it. So $m\angle FCD=(47-6)^{\circ}=41^{\circ}$.

Answer:

$x = 47$
$m\angle FCD=41^{\circ}$