## Geometry: Common Core (15th Edition)

$x = 45$ $y = 60$
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 $y$: $y = 60$