Question

find ( mangle g ) in rhombus ( efgh ).
( h )
( e )
( 6s - 32^circ ) ( g )
( 4s - 48^circ )
( f )
( mangle g = square^circ )
submit

Explanation:

Step1: Use rhombus consecutive angle property

Consecutive angles in a rhombus are supplementary, so:
$$(4s-48^\circ)+(6s-32^\circ)=180^\circ$$

Step2: Simplify and solve for $s$

Combine like terms and isolate $s$:
$$10s - 80^\circ=180^\circ$$
$$10s=260^\circ$$
$$s=26^\circ$$

Step3: Substitute $s$ into $\angle G$ expression

Calculate $m\angle G$ using $6s-32^\circ$:
$$m\angle G=6(26^\circ)-32^\circ$$

Step4: Compute final angle value

Simplify the expression:
$$m\angle G=156^\circ-32^\circ=124^\circ$$

Answer:

$124$