Question

incorrect
your answer is incorrect.
in the figure below, ( mangle abd = 96^circ ), ( mangle cbd = 48^circ ), and ( overline{be} ) bisects ( angle cbd ). find ( mangle abe ).
your answer
image of angle with points a, b, c, d, e
( mangle abe = square^circ )

Explanation:

Step1: Find measure of ∠CBE

Since \( \overline{BE} \) bisects \( \angle CBD \), \( m\angle CBE = m\angle EBD=\frac{1}{2}m\angle CBD \).
Given \( m\angle CBD = 48^\circ \), so \( m\angle CBE=\frac{48^\circ}{2} = 24^\circ \).

Step2: Find measure of ∠ABC

We know \( m\angle ABD = m\angle ABC + m\angle CBD \).
So \( m\angle ABC = m\angle ABD - m\angle CBD \).
Substituting values: \( m\angle ABC = 96^\circ - 48^\circ = 48^\circ \).

Step3: Find measure of ∠ABE

\( m\angle ABE = m\angle ABC + m\angle CBE \).
Substituting values: \( m\angle ABE = 48^\circ + 24^\circ = 72^\circ \).

Answer:

\( 72 \)