Answer
$x = 15$
$y = 25$
Work Step by Step
In a parallelogram, opposite angles are congruent and consecutive angles are supplementary.
$m \angle A + m \angle B = 180$
Let's plug in the knowns:
$(3x + 10) + (8x + 5) = 180$
Group like terms:
$(3x + 8x) + (10 + 5) = 180$
Combine like terms:
$11x + 15 = 180$
Subtract $15$ from each side of the equation to isolate constants on the left side of the equation:
$11x = 165$
Divide each side of the equation by $11$ to solve for $x$:
$x = 15$
Now that we have the value for $x$, we can plug this value into the other equation. Let's set up that equation first:
$m \angle A + m \angle D = 180$
Let's plug in our knowns:
$(3x + 10) + 5y = 180$
Substitute $15$ for $x$:
$3(15) + 10 + 5y = 180$
Multiply first, according to order of operations:
$45 + 10 + 5y = 180$
Add on the left side to simplify:
$55 + 5y = 180$
Subtract $55$ from both sides of the equation to isolate constants on the right side of the equation:
$5y = 125$
Divide each side by $5$ to solve for $y$:
$y = 25$
