Question

if $m\angle bgc = 69^\circ$, then what is $m\angle dga$?
answer attempt 1 out of 2
$m\angle dga =$ $\square$ $^\circ$
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Explanation:

Step1: Identify vertical angles

$\angle BGC$ and $\angle AGD$ are vertical angles, so $m\angle BGC = m\angle AGD = 69^\circ$.

Step2: Identify supplementary angles

$\angle AGD$ and $\angle DGA$ are the same angle? Correction: $\angle BGC$ and $\angle DGA$ are vertical angles. Wait, correct: $\angle BGC$ and $\angle AGD$ (which is $\angle DGA$) are vertical angles, so they are congruent.
Wait, precise step:

Step1: Recognize vertical angle pair

$\angle BGC$ and $\angle DGA$ are vertical angles formed by intersecting lines $AB$ and $CD$. Vertical angles are congruent.
<Expression>
$m\angle BGC = m\angle DGA$
</Expression>

Step2: Substitute given value

Replace $m\angle BGC$ with $69^\circ$.
<Expression>
$m\angle DGA = 69^\circ$
</Expression>

Answer:

$69$