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Math·Geometry and Trigonometry·Lines, angles, and triangles

hard

Note: Figure not drawn to scale.

In the figure, triangle $AEG$ is congruent to triangle $CFD$, where $E$ corresponds to $F$. The measure of angle $ABF$ is $46^{\circ }$. What is the measure, in degrees, of angle $DCF$?

A

$23$

B

$44$

C

$46$

D

$67$