Question

given rhombus vwxy, below, m∠wxz = 60°. if m∠yxz = (-6x + 6)°, solve for x.

Explanation:

Step1: Use the property of a rhombus

In a rhombus, the diagonals bisect the vertex angles. So, \(m\angle WXZ=m\angle YXZ\).

Step2: Set up the equation

Given \(m\angle WXZ = 60^{\circ}\) and \(m\angle YXZ=(-6x + 6)^{\circ}\), we have the equation \(60=-6x + 6\).

Step3: Solve the equation for \(x\)

First, subtract \(6\) from both sides: \(60-6=-6x+6 - 6\), which simplifies to \(54=-6x\).
Then, divide both sides by \(-6\): \(x=\frac{54}{-6}\).

Answer:

\(x=-9\)