Answer:
A. Because the measure of the angle [tex]BCD[/tex] is [tex]19 \°[/tex] and the angles [tex]BCD[/tex] and [tex]ECF[/tex] are Vertical angles. Therefore, they are congruent ( [tex]m\angle BCD=m\angle ECF =19\°[/tex])
B. [tex]m\angle BCD=19\°[/tex]
Step-by-step explanation:
The missing figure is attached.
You can observe in the figure that the parallel lines [tex]k[/tex] and [tex]l[/tex] are intersected by a another line [tex]m[/tex] (this is a transversal).
Let's begin with PART B:
Observe that the angles [tex]ABC[/tex] and [tex]BCD[/tex] are located inside the parallel lines and they alternate sides of the transversal. Therefore, we can determine that these angles are "Alternate Interior Angles".
Since the lines [tex]k[/tex] and [tex]l[/tex] are parallel, we know that the Alternate Interior Angles are congruent. Then:
[tex]m\angle ABC=m\angle BCD=19\°[/tex]
Now we can solve the PART A.
Observe the figure.
Since the angle [tex]BCD[/tex] and the angle [tex]ECF[/tex] share the same vertex, they are "Vertical angles" and, therefore, they are congruent:
[tex]m\angle BCD=m\angle ECF =19\°[/tex]
