Question

$\overrightarrow{bd}$ bisects $\angle abc$, the $m\angle abc = 122^{\circ}$. find $m\angle abd$ and $m\angle dbc$. $m\angle abd = \square^{\circ}$ $m\angle dbc = \square^{\circ}$

Explanation:

Step1: Recall Angle Bisector Definition

An angle bisector divides an angle into two equal parts. So, $\overrightarrow{BD}$ bisecting $\angle ABC$ means $m\angle ABD = m\angle DBC$ and $m\angle ABD + m\angle DBC = m\angle ABC$.

Step2: Calculate Each Angle

Since $m\angle ABC = 122^\circ$ and the two angles are equal, we find each angle by dividing $122^\circ$ by 2. So, $m\angle ABD = m\angle DBC = \frac{122^\circ}{2} = 61^\circ$.

Answer:

$m\angle ABD = \boxed{61}^\circ$
$m\angle DBC = \boxed{61}^\circ$