Question

question 7 of 10 given that abcd is a rhombus, what is the value of (4x - 3)° and x° a. 19.5 b. 45 c. 30 d. 56 e. 18.6 f. cannot be determined

Explanation:

Step1: Recall rhombus property

In a rhombus, the diagonals bisect the angles. So, the angle marked as $x^{\circ}$ and the angle adjacent to $(4x - 3)^{\circ}$ are equal. And the sum of adjacent - interior angles of a rhombus is $180^{\circ}$. Also, the diagonal of a rhombus bisects the vertex - angle. So, $4x-3 = 3x$.

Step2: Solve the equation

\[

$$\begin{align*} 4x-3&=3x\\ 4x-3x&=3\\ x& = 19.5 \end{align*}$$

\]

Answer:

A. 19.5