Question

what is the value of x in the rhombus below? (x + 6)° 2x° a. 28 b. 58 c. 56 d. 24

Explanation:

Step1: Recall property of rhombus

The diagonals of a rhombus bisect the angles of the rhombus. So, in rhombus \(ABCD\), \(\angle ABD=\angle CBD\) and \(\angle BAC = \angle DAC\). Here, we know that the two - angle expressions \((x + 6)^{\circ}\) and \(2x^{\circ}\) are equal because of the angle - bisecting property of the diagonal of a rhombus.
\(x+6 = 2x\)

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides of the equation \(x + 6=2x\).
\(x+6-x=2x - x\)
\(6=x\)

Answer:

D. 24 (There is an error in the above - derived value. Let's correct it. Since the diagonals of a rhombus are perpendicular bisectors of each other, and the sum of adjacent angles in a rhombus is \(180^{\circ}\), and using the angle - bisecting property of diagonals. In right - triangle formed by the diagonals of the rhombus, we know that \(x + 6+2x=90\) (because the diagonals of a rhombus are perpendicular).

Step1: Combine like terms

\(3x+6 = 90\)

Step2: Subtract 6 from both sides

\(3x+6 - 6=90 - 6\)
\(3x=84\)

Step3: Divide both sides by 3

\(x=\frac{84}{3}=28\)

A. 28)