Question

find m∠abc and m∠cbd if m∠abd = 120°

m∠abc =

m∠cbd =

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Explanation:

Step1: Set up equation based on angle addition

Since \(m\angle ABD=m\angle ABC + m\angle CBD\) and \(m\angle ABD = 120^{\circ}\), \(m\angle ABC=2x^{\circ}\), \(m\angle CBD=(5x - 6)^{\circ}\), we have the equation \(2x+(5x - 6)=120\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(2x+5x-6 = 120\), so \(7x-6 = 120\).
Add 6 to both sides: \(7x=120 + 6=126\).
Divide both sides by 7: \(x=\frac{126}{7}=18\).

Step3: Calculate \(m\angle ABC\)

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

Step4: Calculate \(m\angle CBD\)

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

Answer:

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