Question

find the value of x, y, and z in the parallelogram below.
answer
attempt 1 out of 2
x =
y =
z =
(the parallelogram has angles: (y - 1)°, (-x - 10)°, (z - 7)°, and 70°)

Explanation:

Step1: Identify adjacent angles

Adjacent angles in a parallelogram are supplementary. So $70 + (z - 7) = 180$.

Step2: Solve for z

Simplify: $z + 63 = 180 \Rightarrow z = 117$.

Step3: Set opposite angles equal

Opposite angles are equal: $70 = (-x - 10)$ and $z - 7 = y - 1$.

Step4: Solve for x

$-x -10 =70 \Rightarrow -x=80 \Rightarrow x=-80$.

Step5: Solve for y

$117 -7 = y -1 \Rightarrow 110 = y -1 \Rightarrow y=111$.

Answer:

$x=-80$
$y=111$
$z=117$