Question

find the value of z in rhombus bcde. e z + 48° b z z = °

Explanation:

Step1: Recall rhombus property

In a rhombus, adjacent - angles are supplementary, so $\angle B+\angle E = 180^{\circ}$.

Step2: Substitute angle expressions

We know that $\angle B = z$ and $\angle E=z + 48^{\circ}$. Then $z+(z + 48^{\circ})=180^{\circ}$.

Step3: Simplify the equation

Combining like - terms, we get $2z+48^{\circ}=180^{\circ}$.

Step4: Solve for z

Subtract $48^{\circ}$ from both sides: $2z=180^{\circ}-48^{\circ}=132^{\circ}$. Then divide both sides by 2: $z=\frac{132^{\circ}}{2}=66^{\circ}$.

Answer:

$66$