Question

1. if bd bisects ∠abc, and m∠abc=100°, what is m∠abd?

a) 25°
b) 50°
c) 100°
d) 200°

○ a) 25°
○ b) 50°
○ c) 100°
○ d) 200°

Explanation:

Step1: Recall Angle Bisector Definition

An angle bisector divides an angle into two equal parts. So, if \( BD \) bisects \( \angle ABC \), then \( \angle ABD=\angle DBC \) and \( \angle ABC = \angle ABD+\angle DBC = 2\angle ABD \).

Step2: Calculate \( m\angle ABD \)

Given \( m\angle ABC = 100^\circ \), from the bisector property:
\( m\angle ABD=\frac{m\angle ABC}{2} \)
Substitute \( m\angle ABC = 100^\circ \):
\( m\angle ABD=\frac{100^\circ}{2}=50^\circ \)

Answer:

B) \( 50^\circ \)