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 angle - properties

In a rhombus, the diagonals are perpendicular to each other, and a diagonal bisects a pair of opposite angles. Let's assume the properties of angles formed by the diagonals and sides of the rhombus. The sum of the interior angles of a triangle formed by two - sides of the rhombus and a diagonal is 180 degrees. Also, since the diagonals of a rhombus are perpendicular, the angle at the intersection of the diagonals is 90 degrees.
Let's consider one of the four right - angled triangles formed by the diagonals of the rhombus. In a rhombus, the diagonals bisect the angles of the rhombus.
We know that the sum of the angles in a triangle is 180 degrees. In a right - angled triangle formed by the diagonals of the rhombus, if we assume the angles as \(x\), \(y\), and \(z\) where one angle is 90 degrees (the angle between the diagonals), and using the angle - bisecting property of the diagonals of a rhombus, we know that \(x + y=z\) (because of the angle relationships in the right - angled triangle formed by the diagonals and sides of the rhombus).

Answer:

\(x + y=z\)