Question

in the figure below, ( mangle abd = 98^{circ}, mangle ebd = 52^{circ} ), and ( overline{be} ) bisects ( angle cbd ). find ( mangle abc ).

Explanation:

Step1: Find \(m\angle CBD\)

Since \(BE\) bisects \(\angle CBD\), and \(m\angle EBD = 52^{\circ}\), then \(m\angle CBD=2\times m\angle EBD\).
So, \(m\angle CBD = 2\times52^{\circ}=104^{\circ}\).

Step2: Find \(m\angle ABC\)

We know that \(m\angle ABD = 180^{\circ}\) (a straight - angle), and \(m\angle ABD=m\angle ABC + m\angle CBD\).
Then \(m\angle ABC=m\angle ABD - m\angle CBD\).
Substitute \(m\angle ABD = 180^{\circ}\) and \(m\angle CBD = 104^{\circ}\) into the formula: \(m\angle ABC=180^{\circ}-104^{\circ}\).

Answer:

\(76\)