Question

Lines K and L are parallel,and the measure of angle ABC is 19 degrees

Answer 1

Answer:

A. Because the measure of the angle $BCD$ is $19 \°$ and the angles $BCD$  and $ECF$ are Vertical angles. Therefore, they are congruent ( $m\angle BCD=m\angle ECF =19\°$)

B.  $m\angle BCD=19\°$

Step-by-step explanation:

The missing figure is attached.

You can observe in the figure that the parallel lines $k$ and $l$ are intersected by a another line $m$ (this is a transversal).

Let's begin with PART B:

Observe that the angles $ABC$ and $BCD$ 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 $k$ and $l$ are parallel, we know that the Alternate Interior Angles are congruent. Then:

$m\angle ABC=m\angle BCD=19\°$

Now we can solve the PART A.

Observe the figure.

Since the angle $BCD$  and the angle $ECF$ share the same vertex, they are "Vertical angles" and, therefore, they are congruent:

$m\angle BCD=m\angle ECF =19\°$