### Video Transcript

Use the less than, is equal to,
or greater than symbol to complete the statement. If the measure of angle π΄πΆπ΅
equals 62 degrees and the measure of angle π΄ equals 57 degrees, then the
measure of angle π΄π΅π· what the measure of angle π΄πΆπ·.

We notice first that πΆπ· is
equal to π΅π·, so the triangle π΅πΆπ· is an isosceles triangle. Then recalling that the angles
opposite the congruent sides of an isosceles triangle are congruent, we see that
the measures of angles π΅πΆπ· and πΆπ΅π· are equal.

Now, weβre told that the
measure of angle π΄πΆπ΅ is 62 degrees and that the measure of the angle at π΄ is
57 degrees. And recalling that the measures
of the interior angles of a triangle sum to 180 degrees, we have that the
measure of the angle at π΄ and those of angles π΄π΅πΆ and π΄πΆπ΅ sum to 180
degrees.

Substituting the given values
into our equation, we have 57 degrees plus the measure of angle π΄π΅πΆ plus 62
degrees equals 180 degrees. Now, subtracting 57 and 62
degrees from both sides, we find that the measure of angle π΄π΅πΆ equals 61
degrees. We can mark this on our diagram
as shown.

Now, if we call the measure of
our two congruent angles π₯. And making some space, we have
π₯ plus the measure of angle π΄πΆπ· equals 62 degrees. And π₯ plus the measure of
angle π΄π΅π· equals 61 degrees. Now, if we add one to both
sides of the second equation, we have that π₯ plus the measure of angle π΄π΅π·
plus one is equal to 62 degrees.

And now since both of our
right-hand sides equal 62, we can equate our left-hand sides to give π₯ plus the
measure of angle π΄πΆπ· equals π₯ plus the measure of angle π΄π΅π· plus one. Subtracting π₯ from both sides,
we then have the measure of angle π΄πΆπ· equals the measure of angle π΄π΅π· plus
one. This means that the measure of
angle π΄π΅π· is one degree smaller than that of angle π΄πΆπ·. Hence, the measure of angle
π΄π΅π· is less than the measure of angle π΄πΆπ·. And the less than symbol
completes the given statement.