Question

given
$m\angle abd = 70^{circ}$
$m\angle cbd = 5x + 13^{circ}$
$m\angle abc = 3x + 33^{circ}$
find $m\angle abc$:

Explanation:

Step1: Use angle - addition postulate

We know that \(m\angle ABD=m\angle ABC + m\angle CBD\). So, \(70=(3x + 33)+(5x + 13)\).

Step2: Simplify the right - hand side

Combine like terms: \(70 = 3x+5x+33 + 13\), which simplifies to \(70=8x + 46\).

Step3: Solve for \(x\)

Subtract 46 from both sides: \(70−46=8x\), so \(24 = 8x\). Then divide both sides by 8: \(x=\frac{24}{8}=3\).

Step4: Find \(m\angle ABC\)

Substitute \(x = 3\) into the expression for \(m\angle ABC\). \(m\angle ABC=3x + 33\), so \(m\angle ABC=3\times3+33\).
\(m\angle ABC=9 + 33=42^{\circ}\).

Answer:

\(42^{\circ}\)