Question

mixed exercises

1. find ( mangle abc ) and ( mangle cbd ) if ( mangle abd = 120^{circ}).

Explanation:

Step1: Set up the equation

Since \(m\angle ABD=m\angle ABC + m\angle CBD\), we have \(2x+(5x - 6)=120\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+5x-6 = 120\), which gives \(7x-6=120\).

Step3: Solve for \(x\)

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

Step4: Find \(m\angle ABC\)

Substitute \(x = 18\) into \(m\angle ABC=2x\). So \(m\angle ABC=2\times18 = 36^{\circ}\).

Step5: Find \(m\angle CBD\)

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

Answer:

\(m\angle ABC = 36^{\circ}\) and \(m\angle CBD=84^{\circ}\)