Question

angle abc is a straight angle. ( mangle dbc = 130^circ ) and ( overrightarrow{be} ) bisects ( angle abd ). what is ( mangle eba )? (square^circ)

Explanation:

Step1: Find m∠ABD

Since ∠ABC is a straight angle, \( m\angle ABC = 180^\circ \). We know \( m\angle DBC = 130^\circ \), so \( m\angle ABD = m\angle ABC - m\angle DBC = 180^\circ - 130^\circ = 50^\circ \).

Step2: Find m∠EBA

Because \( \overrightarrow{BE} \) bisects \( \angle ABD \), it divides \( \angle ABD \) into two equal angles. So \( m\angle EBA = \frac{1}{2}m\angle ABD = \frac{1}{2} \times 50^\circ = 25^\circ \).

Answer:

25