Question

in the given figure, if ( mangle abd = mangle dbc ) then ( mangle abc = )
( mangle abd ).
( 2(mangle abd) ).
( 3(mangle abd) ).
( mangle dbc ).

Explanation:

Step1: Analyze Angle Composition

From the figure, $\angle ABC$ is composed of $\angle ABD$ and $\angle DBC$, so $m\angle ABC = m\angle ABD + m\angle DBC$.

Step2: Substitute Given Equality

Given $m\angle ABD = m\angle DBC$, substitute $m\angle DBC$ with $m\angle ABD$ in the above equation: $m\angle ABC = m\angle ABD + m\angle ABD = 2(m\angle ABD)$.

Answer:

2(m∠ABD)