Question

the figure shown is a rhombus. which equation is true regarding the angles formed by the diagonals and sides of the rhombus? o x + y = z o 2x = y + z o z + x = 2y o 2x + 2y = 4z

Explanation:

Step1: Recall rhombus properties

In a rhombus, the diagonals are perpendicular bisectors of each other and bisect the angles of the rhombus. Let's assume the properties of angle - relationships. The diagonals of a rhombus are perpendicular, so \(z = 90^{\circ}\). Also, the diagonal of a rhombus bisects the angle of the rhombus.

Step2: Analyze angle - sum in a triangle

In one of the four right - angled triangles formed by the diagonals of the rhombus, the sum of the interior angles of a triangle is \(180^{\circ}\). In a right - angled triangle formed by the diagonals of the rhombus, if one angle is \(z = 90^{\circ}\), and the other two non - right angles are \(x\) and \(y\), then \(x + y+z=180^{\circ}\). Since \(z = 90^{\circ}\), we have \(x + y=90^{\circ}\), so \(x + y=z\).

Answer:

\(x + y = z\)