Answer
$f = 11$
$e = 13$
$c = 204$
Work Step by Step
In parallelograms, opposite sides are congruent, so let's set the expressions for opposite sides equal to one another to solve for $f$:
$f - 3 = 8$
Add $3$ to both sides of the equation to solve for $f$:
$f = 11$
In parallelograms, consecutive angles are supplementary, so let's set the sum of the expressions for the two consecutive angles equal to $180$:
$6e + 102 = 180$
Subtract $102$ from each side of the equation to isolate the constants on the right side of the equation:
$6e = 78$
Divide both sides of the equation by $6$ to solve for $e$:
$e = 13$
Again, we shall use the fact that consecutive angles in a parallelogram are supplementary to solve for $c$. Let's set up that equation:
$6e + \frac{c}{2} = 180$
$6(13) + \frac{c}{2} = 180$
Multiply first, according to order of operations:
$78 + \frac{c}{2} = 180$
$\frac{c}{2} = 102$
Multiply both sides by $2$ to solve for $c$:
$c = 204$
