Question

find the value of x, y, and z in the rhombus below.

Explanation:

Step1: Use the property of adjacent angles in a rhombus (supplementary)

In a rhombus, adjacent angles are supplementary (\(a + b=180^{\circ}\)).
For the angles \((- 10x - 8)^{\circ}\) and \(98^{\circ}\):
\(-10x-8 + 98=180\)
\(-10x+90 = 180\)
\(-10x=180 - 90\)
\(-10x=90\)
\(x=-9\)

Step2: Use the property of opposite angles in a rhombus (equal)

Opposite angles in a rhombus are equal.
For the angles \((-y - 5)^{\circ}\) and \(98^{\circ}\):
\(-y-5=98\)
\(-y=98 + 5\)
\(-y=103\)
\(y=-103\)

Step3: Use the property of adjacent angles (supplementary) again

For the angles \((-2z + 8)^{\circ}\) and \(98^{\circ}\):
\(-2z+8+98 = 180\)
\(-2z+106=180\)
\(-2z=180 - 106\)
\(-2z=74\)
\(z=-37\)

Answer:

\(x=-9\), \(y = - 103\), \(z=-37\)