Question

for what value of x is the figure a rhombus? the value of x is \boxed{}. (simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Use rhombus diagonal property

Diagonals bisect angles, so adjacent angles sum to 180°. Thus, $(18x + 1) + (3x + 1) = 180$.

Step2: Simplify the equation

Combine like terms: $21x + 2 = 180$.

Step3: Solve for x

Subtract 2: $21x = 178$. Divide by 21: $x = \frac{178}{21}$.

Answer:

$\frac{178}{21}$