Question

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

Explanation:

Step1: Recall the property of rhombus diagonals

The diagonals of a rhombus are perpendicular to each other. So the triangle formed by the diagonals and the side of the rhombus is a right - triangle. In a right - triangle, the sum of the two non - right angles is equal to the right angle.

Step2: Analyze the angles

In the right - triangle formed by the diagonals and the side of the rhombus, we have \(x + y=z\) (because in a right - triangle, the sum of two acute angles (\(x\) and \(y\)) is equal to the right angle (\(z = 90^{\circ}\))).

Answer:

\(x + y=z\)