### Video Transcript

In the figure, triangle π·π΅πΆ is
symmetrical about line πΏ. If the measure of angle πΆ is 69
degrees, what is the measure of angle π΄π΅π·?

Weβre told that triangle π·π΅πΆ is
symmetrical about line πΏ. So itβs a mirror image over this
line. We are also told that the measure
of angle πΆ is 69 degrees, and we want to find the measure of angle π΄π΅π·.

Itβs very important that triangle
π·π΅πΆ is symmetrical about line πΏ, because if the measure of angle πΆ is 69
degrees, the measure of angle πΆπ·π΅ must also be 69 degrees. And this is because if we would
take our yellow triangle and fold it over the blue line, those angles would land on
top of each other, should they- should be the exact same 69 degrees. And this is helpful for a few
reasons.

All angles of triangle π·π΅πΆ must
add up to be 180 degrees, because a triangle always does. So we can find this last angle of
the triangle by setting 69 plus 69 plus π₯ equal to 180 degrees. 69 plus 69 is 138, and if we
subtract 138 from both sides of the equation, we find that π₯ is equal to 42
degrees.

So how will this help us find the
measure of angle π΄π΅π·? Well, the measure of angle π΅
completely is 90 degrees, because of that box. So if we can call our missing angle
π¦, then that angle plus 42 should equal 90. So to solve for π¦, we need to
subtract 42 from both sides of the equation, resulting in that angle equaling 48
degrees. Therefore, the measure of angle
π΄π΅π· is equal to 48 degrees.