Question

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

Explanation:

Step1: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal.
So, \(x - 1=110\)
\(x=110 + 1\)
\(x = 111\)

Step2: Use the property of consecutive angles in a parallelogram

Consecutive angles in a parallelogram are supplementary (sum to \(180^{\circ}\)).
So, \((-y + 2)+110=180\)
\(-y+112 = 180\)
\(-y=180 - 112\)
\(-y = 68\)
\(y=-68\)

Step3: Use the property of opposite angles (again)

Since \(-6z - 2=-y + 2\), and \(y=-68\)
Substitute \(y=-68\) into \(-6z - 2=-y + 2\)
\(-6z-2=-(-68)+2\)
\(-6z-2=68 + 2\)
\(-6z-2=70\)
\(-6z=70 + 2\)
\(-6z=72\)
\(z=\frac{72}{-6}\)
\(z=-12\)

Answer:

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