Question

Look at this diagram:

A
B
C
D
E
F
G
H


If
BD
and
EG
are parallel lines and mEFH= 66°, what is mEFC?

Answer 1

To find \( mEFC \), we can use the relationships between the angles formed by the transversals and the parallel lines \( BD \) and \( EG \).

Since \( BD \) and \( EG \) are parallel, the angles formed between any transversal crossing the two lines will have certain properties. We know that \( mEFH = 66^\circ \).

The angle \( EFC \) is on the same side of the transversal \( EF \) as \( EFH \). Therefore, by the Consecutive Interior Angles Theorem (which states that consecutive interior angles are supplementary when two parallel lines are cut by a transversal), we can write:

\[
mEFC + mEFH = 180^\circ
\]

Substituting the known value of \( mEFH \):

\[
mEFC + 66^\circ = 180^\circ
\]

To find \( mEFC \), we will subtract \( 66^\circ \) from \( 180^\circ \):

\[
mEFC = 180^\circ - 66^\circ = 114^\circ
\]

Thus, the measure of angle \( EFC \) is \( mEFC = 114^\circ \).