Question

in the figure below, ( mangle abd = 118^{circ}, mangle ebd = 34^{circ} ), and ( overline{be} ) bisects ( angle cbd ). find ( mangle abc ).

Explanation:

Step1: Find \(m\angle CBD\)

Since \(BE\) bisects \(\angle CBD\), then \(m\angle CBD = 2\times m\angle EBD\).
Given \(m\angle EBD=34^{\circ}\), so \(m\angle CBD = 2\times34^{\circ}=68^{\circ}\).

Step2: Find \(m\angle ABC\)

We know that \(m\angle ABD=m\angle ABC + m\angle CBD\).
Given \(m\angle ABD = 118^{\circ}\) and \(m\angle CBD=68^{\circ}\), then \(m\angle ABC=m\angle ABD - m\angle CBD\).
Substitute the values: \(m\angle ABC=118^{\circ}-68^{\circ}\).

Answer:

\(50\)