Question

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

A.explain why the measure of angle ECF is 19 degrees



B.what is the measure of angle BCD?explain.

Answer 1

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\°`

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\°`