Question

in the figure below, ( mangle abd = 81^circ ), ( mangle ebd = 20^circ ), and ( overline{be} ) bisects ( angle cbd ). find ( mangle abc )

Explanation:

Step1: Find \( m\angle CBD \)

Since \( \overline{BE} \) bisects \( \angle CBD \), \( m\angle CBD = 2\times m\angle EBD \). Given \( m\angle EBD = 20^\circ \), so \( m\angle CBD = 2\times20^\circ = 40^\circ \).

Step2: Find \( m\angle ABC \)

We know \( m\angle ABD = 81^\circ \) and \( m\angle CBD = 40^\circ \). Then \( m\angle ABC = m\angle ABD - m\angle CBD \). Substituting the values, we get \( m\angle ABC = 81^\circ - 40^\circ = 41^\circ \).

Answer:

\( 41 \)