Question

find the value of x, y, and z in the rhombus below.
answer attempt 2 out of 2
x = y = z =

Explanation:

Step1: Use the property of opposite angles in a rhombus

In a rhombus, opposite angles are equal.
So, \(-3x + 6=72\)
\(-3x=72 - 6\)
\(-3x=66\)
\(x=\frac{66}{-3}=- 22\)

Step2: Use the property of adjacent angles in a rhombus

Adjacent angles in a rhombus are supplementary (\(180^{\circ}\)).
For \(-y + 4\) and \(72^{\circ}\), \((-y + 4)+72 = 180\)
\(-y+76 = 180\)
\(-y=180 - 76\)
\(-y = 104\)
\(y=-104\)

For \(-z - 10\) and \(72^{\circ}\), \((-z - 10)+72=180\)
\(-z + 62=180\)
\(-z=180 - 62\)
\(-z=118\)
\(z=-118\)

Answer:

\(x=-22\), \(y = - 104\), \(z=-118\)