Answer
$a = 8$
$h = 30$
$k = 120$
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 $a$:
$a + 15 = 23$
Subtract $15$ from both sides of the equation to solve for $a$:
$a = 8$
In parallelograms, consecutive angles are supplementary, so let's set the sum of the expressions for the two consecutive angles equal to $180$:
$4h + 2h = 180$
Combine like terms:
$6h = 180$
Divide both sides of the equation by $6$ to solve for $h$:
$h = 30$
Again, we shall use the fact that consecutive angles in a parallelogram are supplementary to solve for $k$. Let's set up that equation:
$2h + k = 180$
$2(30) + k = 180$
Multiply first, according to order of operations:
$60 + k = 180$
Subtract $60$ from each side of the equation to solve for $k$:
$k = 120$
