Question

in the figure below, m∠abd = 89°, m∠ebd = 24°, and be bisects ∠cbd. find m∠abc. m∠abc = \\(\square\\)°

Explanation:

Step1: Find m∠CBD

Since \( \overline{BE} \) bisects \( \angle CBD \), \( m\angle CBD = 2 \times m\angle EBD \). Given \( m\angle EBD = 24^\circ \), so \( m\angle CBD = 2 \times 24^\circ = 48^\circ \).

Step2: Calculate m∠ABC

We know \( m\angle ABD = 89^\circ \) and \( m\angle CBD = 48^\circ \). Then \( m\angle ABC = m\angle ABD - m\angle CBD \). Substitute the values: \( m\angle ABC = 89^\circ - 48^\circ = 41^\circ \).

Answer:

\( 41 \)