Question

m∠abd = 86°. find m∠abc

Explanation:

Step1: Set up the angle equation

From the diagram, we know that \( m\angle ABC = m\angle ABD + m\angle DBC \). We are given \( m\angle ABD = 86^\circ \), \( m\angle ABD=2x - 4\), and \( m\angle DBC=x - 10\). So first, we set \( 2x-4 = 86\) to find \( x\).
\[2x-4 = 86\]

Step2: Solve for \( x\)

Add 4 to both sides of the equation:
\[2x=86 + 4\]
\[2x=90\]
Divide both sides by 2:
\[x=\frac{90}{2}=45\]

Step3: Find \( m\angle DBC\)

Substitute \( x = 45\) into \( m\angle DBC=x - 10\):
\[m\angle DBC=45-10 = 35^\circ\]

Step4: Find \( m\angle ABC\)

Since \( m\angle ABC=m\angle ABD + m\angle DBC\), substitute \( m\angle ABD = 86^\circ\) and \( m\angle DBC = 35^\circ\):
\[m\angle ABC=86+35=121^\circ\]

Answer:

\(121^\circ\)