Question

mixed exercises

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

Explanation:

Step1: Set up the angle sum equation

Since \( \angle ABC + \angle CBD=\angle ABD \), we substitute the given angle expressions. So \( 2x+(5x - 6)=120 \).

Step2: Solve for \( x \)

Combine like terms: \( 7x-6 = 120 \). Add 6 to both sides: \( 7x=120 + 6=126 \). Divide both sides by 7: \( x=\frac{126}{7} = 18 \).

Step3: Find \( m\angle ABC \)

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

Step4: Find \( m\angle CBD \)

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

Answer:

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