Question

1. $overrightarrow{bd}$ bisects $angle abc$ and the $mangle abd = 57^circ$, find $mangle dbc$ and $mangle abc$.

$mangle dbc = square^circ$
$mangle abc = square^circ$

Explanation:

Step1: Recall Angle Bisector Definition

An angle bisector divides an angle into two equal parts. So, if \(\overrightarrow{BD}\) bisects \(\angle ABC\), then \(\angle ABD=\angle DBC\).
Given \(m\angle ABD = 57^\circ\), so \(m\angle DBC=m\angle ABD = 57^\circ\).

Step2: Calculate \(m\angle ABC\)

Since \(\angle ABC=\angle ABD+\angle DBC\), substitute the values of \(\angle ABD\) and \(\angle DBC\).
\(m\angle ABC = 57^\circ+ 57^\circ=114^\circ\).

Answer:

\(m\angle DBC = \boldsymbol{57}\) \(^\circ\)
\(m\angle ABC = \boldsymbol{114}\) \(^\circ\)