Question

m∠cbd if m∠abd = 120°.

Explanation:

Step1: Set up equation

Since \(m\angle ABD=m\angle ABC + m\angle CBD\), we have \(120^{\circ}=2x+(5x - 6)\).
Simplify the right - hand side: \(120=2x + 5x-6\), which is \(120 = 7x-6\).

Step2: Solve for \(x\)

Add \(6\) to both sides: \(120 + 6=7x\), so \(126 = 7x\).
Divide both sides by \(7\): \(x=\frac{126}{7}=18\).

Step3: Find \(m\angle CBD\)

Substitute \(x = 18\) into \(5x-6\).
\(m\angle CBD=5\times18-6\).
\(m\angle CBD=90 - 6=84^{\circ}\).

Answer:

\(84^{\circ}\)