Question

in triangle abc, segment bd is the angle bisector. if angle abc measures 110 degrees, what is the measure of angle abd?
a. 65 degrees
b. 55 degrees
c. 110 degrees
d. 45 degrees

Explanation:

Step1: Recall angle bisector definition

An angle bisector divides an angle into two equal parts. So, \( \angle ABD=\angle DBC \), and \( \angle ABC = \angle ABD+\angle DBC \).

Step2: Calculate \( \angle ABD \)

Since \( \angle ABC = 110^\circ \) and \( \angle ABD=\angle DBC \), we can write \( \angle ABC = 2\angle ABD \). Then, \( \angle ABD=\frac{\angle ABC}{2}=\frac{110^\circ}{2} = 55^\circ \).

Answer:

B. 55 degrees