Question

find the value of $x$, $y$, and $z$ in the parallelogram below.
answer
attempt 1 out of 6
$x = square$
$y = square$
$z = square$

Explanation:

Step1: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal.
So, \(z + 10=80\)
\(z=80 - 10\)
\(z = 70\)

Step2: Use the property of consecutive angles in a parallelogram

Consecutive angles in a parallelogram are supplementary (sum to \(180^{\circ}\)).
For \(80^{\circ}\) and \((-3x - 2)^{\circ}\):
\(80+(-3x - 2)=180\)
\(-3x+78 = 180\)
\(-3x=180 - 78\)
\(-3x=102\)
\(x=\frac{102}{-3}\)
\(x=- 34\)

For \(80^{\circ}\) and \((-y + 6)^{\circ}\):
\(80+(-y + 6)=180\)
\(-y+86 = 180\)
\(-y=180 - 86\)
\(-y = 94\)
\(y=-94\)

Answer:

\(x=-34\), \(y = - 94\), \(z = 70\)