Question

in the figure below, \\( \overline { d e } \\) bisects \\( \angle a e b \\). what is the measure of \\( \angle d e a? \\)

a \\( 15 ^ { \circ } \\)
b \\( 30 ^ { \circ } \\)
c \\( 40 ^ { \circ } \\)
d \\( 60 ^ { \circ } \\)

Explanation:

Step1: Find the measure of ∠AEB

A full - circle angle is \(360^{\circ}\). Given that the non - ∠AEB part is \(300^{\circ}\), so \(\angle AEB=360^{\circ}-300^{\circ}=60^{\circ}\).

Step2: Use the angle - bisector property

Since \(\overline{DE}\) bisects \(\angle AEB\), by the definition of an angle bisector (\(\angle DEA=\angle DEB=\frac{1}{2}\angle AEB\)). Substitute \(\angle AEB = 60^{\circ}\) into the formula, we get \(\angle DEA=\frac{1}{2}\times60^{\circ}=30^{\circ}\).

Answer:

B. \(30^{\circ}\)