Question

find ( mangle c ) in rhombus ( bcde ).( mangle c = square^circ )submit

Explanation:

Step1: Use rhombus consecutive angles property

In a rhombus, consecutive angles are supplementary, so:
$$(3z-18^\circ)+(3z+54^\circ)=180^\circ$$

Step2: Simplify and solve for z

Combine like terms and isolate z:
$$6z + 36^\circ = 180^\circ$$
$$6z = 180^\circ - 36^\circ$$
$$6z = 144^\circ$$
$$z = \frac{144^\circ}{6} = 24^\circ$$

Step3: Find $m\angle E$ first

Substitute z into $\angle E$ expression:
$$m\angle E = 3(24^\circ)-18^\circ = 72^\circ - 18^\circ = 54^\circ$$

Step4: Use rhombus opposite angles property

In a rhombus, opposite angles are equal, so $m\angle C = m\angle E$.

Answer:

$54^\circ$