### Video Transcript

In the given circle with center π,
chords π΄π΅ and πΆπ· are parallel and the measure of angle π΅ππ· is equal to 74
degrees. Find the measure of angle
π΄πΈπΆ.

To answer this question, weβre
going to use three theorems about circles.

The first tells us that the
measures of the arcs between two parallel chords are equal. Applied to our circle, since chords
π΄π΅ and πΆπ· are parallel, this means that the measures of arcs π΅π· and π΄πΆ are
equal.

The second theorem we can use to
find the measure of angle π΄πΈπΆ tells us that when two angles are subtended by the
same arc, the measure of the angle at the center of the circle is twice the measure
of the angle at the circumference. Applied to our circle, this means
that any angle at the circumference subtended by the arc π΅π· must be half the
measure of the angle subtended by π΅π· at the center. If we call a point on the
circumference πΉ, then the measure of angle π΅πΉπ· is then one-half the measure of
angle π΅ππ·. Thatβs one-half of 74 degrees,
which is 37 degrees.

Our third theorem is that angles
subtended by the same arc at the circumference have equal measure. Now how weβre going to apply this
to our circle is by using the fact we noted earlier from the first theorem that arcs
π΅π· and π΄πΆ are equal. This being the case, any angle
subtended by arc π΅π· at the circumference will be equal in measure to any angle at
the circumference subtended by arc π΄πΆ. So the measure of angle π΅πΉπ· we
found earlier using the second theorem will be equal to the measure of angle π΄πΈπΆ,
since angle π΄πΈπΆ is subtended by arc π΄πΆ. And thatβs 37 degrees.

Hence, if chords π΄π΅ and πΆπ· are
parallel and the measure of angle π΅ππ· is 74 degrees, then the measure of angle
π΄πΈπΆ is equal to 37 degrees.