### Video Transcript

Triangle π΄π΅πΆ has been drawn between two parallel lines. The triangleβs sides have been extended as shown. By finding the values of π₯ and π¦, show that triangle π΄π΅πΆ is isosceles.

First, we need to make sure that we know that this diagram is not drawn to scale. So weβll use what we know about intersecting lines to help us identify these angle measures. Angle πΆπ΅π΄ can be found because we know that angles on a straight line must sum to 180 degrees. If this measure is 80 degrees, then πΆπ΅π΄ must measure 100 degrees. Weβll say angle πΆπ΅π΄ measures 100 degrees because angles on a straight line sum to 180 degrees.

What about this angle, angle π΅πΆπ΄? Angle π΅πΆπ΄ has an alternate exterior angle. And alternate exterior angles are equal. Angle π΅πΆπ΄ must be 40 degrees. π¦ is angle π΅πΆπ΄. It equals 40 degrees because alternate angles are equal.

The last value weβre missing is the value for π₯. But we know that, inside a triangle, all three angles must sum to 180 degrees. So we take 180 degrees. And we subtract 140 degrees, which is the other two angles combined. 180 degrees minus 140 degrees equals 40 degrees. π₯ equals angle π΅π΄πΆ. And that equals 40 degrees because angles in a triangle sum to 180 degrees. Weβre trying to prove that triangle π΄π΅πΆ is isosceles. An isosceles triangle has two equal angles. For us, π₯ and π¦ are both 40 degrees.

Since π¦ equals π₯, we can say that the triangle π΄π΅πΆ is isosceles.