Question

bd bisects ∠abc and the m∠abd = 57°. find m∠dbc and m∠abc.
m∠dbc =

m∠abc =

Explanation:

Step1: Recall angle - bisector definition

An angle - bisector divides an angle into two equal angles. Since $\overrightarrow{BD}$ bisects $\angle ABC$, then $\angle ABD=\angle DBC$.

Step2: Find $m\angle DBC$

Given $m\angle ABD = 57^{\circ}$, and $\angle ABD=\angle DBC$, so $m\angle DBC=57^{\circ}$.

Step3: Find $m\angle ABC$

Since $\angle ABC=\angle ABD+\angle DBC$ and $\angle ABD = \angle DBC=57^{\circ}$, then $m\angle ABC=57^{\circ}+57^{\circ}=114^{\circ}$.

Answer:

$m\angle DBC = 57^{\circ}$
$m\angle ABC = 114^{\circ}$