Answer
$x = 45$
$y = 60$
Work Step by Step
Adjacent angles of a parallelogram are supplementary. We can set the two adjacent angles equal to $180^{\circ}$ and solve for $x$:
$m \angle A + m \angle B = 180$
Plug in expressions given for the angles:
$(2x + 10) + (2x - 10) = 180$
Add like terms on the left side of the equation, making sure to pay attention to the signs:
$4x = 180$
Divide both sides of the equation by $4$ to solve for $x$:
$x = 45$
We also know that in a parallelogram, opposite angles are congruent, so let's set opposite angles equal to one another:
$m \angle B = m \angle D$
Plug in expressions given:
$2x - 10 = y + 20$
Plug in $45$ for $x$:
$2(45) - 10 = y + 20$
Multiply first, according to order of operations:
$90 - 10 = y + 20$
Subtract on the left side of the equation to simplify:
$80 = y + 20$
Subtract $20$ from each side of the equation to solve for $y$:
$y = 60$
