### Video Transcript

Find the measure of angle
π΄πΆπ΅.

Letβs have a closer look at the
figure weβve been given. There is a triangle formed by
connecting the points π΄, π΅, and πΆ. The measure of one of the interior
angles in this triangle, angle π΄π΅πΆ, has been marked as 35 degrees. And the measure of the angle weβve
been asked to calculate, angle π΄πΆπ΅, has been marked as π₯. Weβre also given the measure of an
angle outside the triangle, which is 65 degrees. The final thing to note is that
line π΅π΄ and line πΆπ·, as weβve now labeled it, are parallel, as indicated by the
arrows along their lengths.

Now, we need to consider how we can
use all this information to determine the measure of angle π΄πΆπ΅. Because lines π΅π΄ and πΆπ· are
parallel, angle π΄πΆπ· and angle πΆπ΄π΅ are alternate angles. Alternate angles are of equal
measure, so this tells us that the measure of angle πΆπ΄π΅ is also 65 degrees.

We now know the measures of two of
the interior angles in triangle π΄π΅πΆ, and we wish to calculate the measure of the
third. We can recall that the sum of the
measures of the interior angles in any triangle is 180 degrees. We can therefore form an equation
using the measures of the interior angles of triangle π΄π΅πΆ. π₯ plus 35 degrees plus 65 degrees
equals 180 degrees. This equation simplifies to π₯ plus
100 degrees equals 180 degrees. π₯ is therefore equal to 180
degrees minus 100 degrees, which is 80 degrees.

Remember π₯ represents the measure
of angle π΄πΆπ΅. So using the sum of the measures of
the interior angles in a triangle, we found that the measure of angle π΄πΆπ΅ is 80
degrees.