Question

find ( mangle g ) in rhombus ( fghi ).
( mangle g = square^circ )

Explanation:

Step1: Use rhombus consecutive angle property

Consecutive angles in a rhombus are supplementary, so:
$$(3z+18^\circ)+(4z-76^\circ)=180^\circ$$

Step2: Simplify and solve for $z$

Combine like terms and isolate $z$:
$$7z - 58^\circ=180^\circ$$
$$7z=238^\circ$$
$$z=\frac{238^\circ}{7}=34^\circ$$

Step3: Calculate $m\angle G$

Substitute $z=34^\circ$ into $4z-76^\circ$:
$$m\angle G=4(34^\circ)-76^\circ$$

Answer:

$60^\circ$