the figure shown is a rhombus. which equation is true regarding the angles formed by the diagonals and sides…

Explanation:

Step1: Recall rhombus properties

In a rhombus, the diagonals bisect the angles of the rhombus and are perpendicular to each other. Let's consider the angle - sum property of a triangle formed by the diagonals and sides of the rhombus. The diagonals of a rhombus are perpendicular, so the angle between the diagonals is 90 degrees. Also, the diagonal of a rhombus bisects the vertex - angle of the rhombus. Let's assume that the diagonal bisects the vertex - angle. If we consider a triangle formed by two sides of the rhombus and a diagonal, we know that the exterior - angle property of a triangle states that the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In the rhombus, the diagonal bisects the angle of the rhombus. Let the angle of the rhombus be (2y). The two angles formed by the diagonal and the sides of the rhombus are (x) and (z). Since the diagonal bisects the angle of the rhombus, we have (y = x) and also, considering the right - angled triangle formed by the diagonals of the rhombus, we know that (z = 90^{\circ}-x). We know that the sum of the interior angles of a triangle formed by two sides of the rhombus and a diagonal gives us the relationship. The diagonal of a rhombus bisects the vertex - angle. So, if we consider the relationship between the angles (x), (y), and (z), we know that (x + y=z) because of the angle - sum property of a right - angled triangle formed by the diagonals and sides of the rhombus.

Answer:

A. (x + y=z)