Question

question 1 of 10 given that abcd is a rhombus, what is the value of

a. 29
b. 23
c. 46
d. 38
e. 45
f. cannot be determined

Explanation:

Step1: Recall rhombus property

In a rhombus, the diagonals bisect the angles. So, the angle \((4x - 25)^{\circ}\) and \(x^{\circ}\) are equal, i.e., \(4x-25=x\).

Step2: Solve the equation

Subtract \(x\) from both sides: \(4x - x-25=x - x\), which gives \(3x-25 = 0\). Then add 25 to both sides: \(3x-25 + 25=0 + 25\), so \(3x=25\). Divide both sides by 3: \(x=\frac{25}{3}\) is incorrect. The correct equation - since the adjacent - angles of a rhombus are supplementary and the diagonals bisect the angles, we know that the two - given angles are equal. So \(4x-25=x\). Rearranging gives \(4x - x=25\), \(3x = 87\), and \(x = 29\).

Answer:

A. 29