Question

figure abcd is a rhombus where m∠abc = 84° and m∠abe = 3x - 6. solve for x.

Explanation:

Step1: Recall rhombus property

In a rhombus, the diagonal bisects the vertex - angle. So, $\angle ABE=\frac{1}{2}\angle ABC$.

Step2: Substitute the given angle - measures

Given $\angle ABC = 84^{\circ}$ and $\angle ABE=3x - 6$, we have the equation $3x - 6=\frac{84}{2}$.

Step3: Simplify the right - hand side of the equation

$\frac{84}{2}=42$, so the equation becomes $3x - 6 = 42$.

Step4: Solve for x

Add 6 to both sides of the equation: $3x-6 + 6=42 + 6$, which simplifies to $3x=48$. Then divide both sides by 3: $x=\frac{48}{3}=16$.

Answer:

16