ABCD 是一个菱形。$\angle BAC = 51^\circ$。$\angle x$ 和 $\angle y$ 的和是多少？ 答案：___ $^\circ$

1. Find angle x using properties of parallel lines in a rhombus

In a rhombus, opposite sides are parallel ($AB \parallel DC$).
Therefore, alternate interior angles are equal.
$\angle x = \angle ACD = \angle BAC = 51^\circ$

2. Find angle y using properties of a rhombus

In a rhombus, the diagonal bisects the interior angles.
So, $\angle DAB = 2 \times \angle BAC = 2 \times 51^\circ = 102^\circ$.
Consecutive interior angles in a rhombus (or any parallelogram) add up to $180^\circ$.
$\angle y = \angle ABC = 180^\circ - \angle DAB = 180^\circ - 102^\circ = 78^\circ$.

3. Calculate the sum of angle x and angle y

$\angle x + \angle y = 51^\circ + 78^\circ = 129^\circ$