Question

question 4 of 10 given that abcd is a rhombus, what is the value of x? a. 18.25 b. 20.75 c. 30 d. 64

Explanation:

Step1: Recall rhombus property

In a rhombus, the diagonals bisect the angles of the rhombus. So, $\angle BAC=\angle DAC$. We have the equation $x = 3x + 7$.

Step2: Solve the equation

Subtract $3x$ from both sides: $x-3x=3x + 7-3x$. This gives $-2x=7$. Then divide both sides by $- 2$: $x=-\frac{7}{2}$. But this is wrong. The correct property is that adjacent - angles of a rhombus are supplementary and the diagonals are perpendicular bisectors. Also, the angles formed by the diagonals and the sides of the rhombus are related as follows: In a rhombus, the diagonals bisect the vertex - angles. So, we know that $\angle BAC$ and $\angle DAC$ are equal. The correct equation should be $x+(3x + 7)=90$ (because the diagonals of a rhombus are perpendicular).

Step3: Simplify the new equation

Combine like - terms: $4x+7 = 90$.

Step4: Isolate the variable

Subtract 7 from both sides: $4x+7 - 7=90 - 7$, which gives $4x=83$.

Step5: Solve for x

Divide both sides by 4: $x=\frac{83}{4}=20.75$.

Answer:

B. 20.75