Question

dcba is a rhombus. if m∠boa = 6x + 3, find x.

Explanation:

Step1: Recall rhombus diagonals property

In a rhombus, the diagonals are perpendicular to each other. So, \( \angle BOA = 90^\circ \).

Step2: Set up the equation

We know \( m\angle BOA = 6x + 3 \) and \( \angle BOA = 90^\circ \), so we set up the equation:
\( 6x + 3 = 90 \)

Step3: Solve for \( x \)

Subtract 3 from both sides: \( 6x = 90 - 3 = 87 \)
Divide both sides by 6: \( x=\frac{87}{6}=\frac{29}{2} = 14.5 \)

Answer:

\( x = 14.5 \) (or \( x=\frac{29}{2} \))