Question

if $mangle afb = 5x - 10$ and $mangle bfc = 3x + 20$, find $x$.

Explanation:

Step1: Set up the equation

Since $\angle AFB$ and $\angle BFC$ are supplementary (assuming $\angle AFC$ is a straight - angle and $\angle AFB+\angle BFC = 180^{\circ}$), we have the equation $(5x - 10)+(3x + 20)=180$.

Step2: Combine like terms

$5x+3x-10 + 20=180$, which simplifies to $8x+10 = 180$.

Step3: Isolate the variable term

Subtract 10 from both sides of the equation: $8x=180 - 10$, so $8x=170$.

Step4: Solve for x

Divide both sides by 8: $x=\frac{170}{8}=\frac{85}{4}=21.25$.

Answer:

$x = 21.25$