Question

find x, y, and z in the parallelogram below.
the parallelogram has angles: (-4x + 4)°, (6 - 7y)°, (x - 9)°, and 75°.
answer
x =
y =
z =

Explanation:

Step1: Use parallelogram opposite angles property

Opposite angles in a parallelogram are equal, so set $x+9 = 76$.
Solve for $x$: $x = 76 - 9 = 67$

Step2: Use parallelogram consecutive angles property

Consecutive angles in a parallelogram are supplementary (sum to $180^\circ$). Set $4z+4 + 76 = 180$.
Simplify: $4z + 80 = 180$
Solve for $z$: $4z = 180 - 80 = 100$, so $z = \frac{100}{4} = 25$

Step3: Use parallelogram opposite angles property

Opposite angles in a parallelogram are equal, so set $y-7 = 76$.
Solve for $y$: $y = 76 + 7 = 83$

Answer:

$x = 67$, $y = 83$, $z = 25$