Question

find the value of x, y, and z in the rhombus below. 120° (-y+7)° (-3x+6)° (7z+4)°

Explanation:

Step1: Use rhombus adjacent angles

Adjacent angles sum to 180°. So $120 + (-3x + 6) = 180$.
$-3x + 126 = 180$ → $-3x = 54$ → $x = -18$.

Step2: Use rhombus opposite angles

Opposite angles equal. So $120 = (-y + 7)$? No, wait: the other pair of opposite angles: $(-3x +6) = (7z +4)$.
Substitute $x=-18$: $-3(-18)+6=54+6=60$. So $60=7z+4$ → $7z=56$ → $z=8$.
The angle $(-y+7)$ is opposite to $120°$? No, adjacent to $60°$: $(-y+7)+60=180$ → $-y=113$ → $y=-113$.

Answer:

$x=-18$, $y=-113$, $z=8$