Question

learning target: apply the angle addition postulate to find a missing angle. given: m∠abc = 3x + 3, m∠cbd = 6x + 1, m∠abd = 40°. find: m∠cbd and m∠abc. given: ∠bac = 2x + 11, ∠cad = x + 13, m∠bad = 60°. find: m∠bac. given: m∠esr = 9x - 2, m∠tsr = 38x - 3, m∠tse = 115. find: m∠tsr

Explanation:

Step1: Use angle - addition postulate

We know that \(m\angle ABD=m\angle ABC + m\angle CBD\). Given \(m\angle ABD = 40^{\circ}\), \(m\angle ABC=3x + 3\), and \(m\angle CBD=6x + 1\). So, \((3x + 3)+(6x + 1)=40\).

Step2: Combine like - terms

\(3x+6x+3 + 1=40\), which simplifies to \(9x+4 = 40\).

Step3: Solve for \(x\)

Subtract 4 from both sides: \(9x=40 - 4=36\). Then divide both sides by 9: \(x = \frac{36}{9}=4\).

Step4: Find \(m\angle ABC\)

Substitute \(x = 4\) into the formula for \(m\angle ABC\): \(m\angle ABC=3x + 3=3\times4+3=12 + 3=15^{\circ}\).

Step5: Find \(m\angle CBD\)

Substitute \(x = 4\) into the formula for \(m\angle CBD\): \(m\angle CBD=6x + 1=6\times4+1=24 + 1=25^{\circ}\).

Answer:

\(m\angle ABC = 15^{\circ}\), \(m\angle CBD=25^{\circ}\)