Question

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

Explanation:

Step1: Find \(m\angle ABD\)

Since \(\angle ABC\) is a straight angle (\(m\angle ABC = 180^{\circ}\)) and \(m\angle DBC=130^{\circ}\), then \(m\angle ABD=m\angle ABC - m\angle DBC\).
\(m\angle ABD = 180^{\circ}-130^{\circ}=50^{\circ}\)

Step2: Use the angle - bisector property

Because \(BE\) bisects \(\angle ABD\), by the definition of an angle - bisector (\(m\angle EBA=\frac{1}{2}m\angle ABD\))
Substitute \(m\angle ABD = 50^{\circ}\) into the formula: \(m\angle EBA=\frac{1}{2}\times50^{\circ}\)

Answer:

\(25\)