Question

find the value of x, y, and z in the parallelogram below.
answer attempt 1 out of 2
x = y = z =

Explanation:

Step1: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal.
So, \(x - 1=110\)

Step2: Solve for \(x\)

Add \(1\) to both sides of the equation \(x - 1=110\)
\(x=110 + 1\)
\(x = 111\)

Step3: Use the property of consecutive angles in a parallelogram

Consecutive angles in a parallelogram are supplementary (\(a + b=180^{\circ}\)).
So, \((-y + 2)+110 = 180\)

Step4: Solve for \(y\)

First, simplify the left - hand side: \(-y+2 + 110=-y + 112\)
Then, \(-y+112 = 180\)
Subtract \(112\) from both sides: \(-y=180 - 112\)
\(-y = 68\), so \(y=-68\)

Step5: Use the property of opposite angles (another pair)

Since \((-6z - 2)=(-y + 2)\) (opposite angles). Substitute \(y=-68\)
\(-6z-2=-(-68)+2\)
\(-6z-2 = 68 + 2\)
\(-6z-2=70\)
Add \(2\) to both sides: \(-6z=70 + 2\)
\(-6z=72\)
Divide both sides by \(-6\): \(z=\frac{72}{-6}=-12\)

Answer:

\(x = 111\), \(y=-68\), \(z=-12\)