### Video Transcript

In the figure, π΄π΅πΆπ· and πΆπ΅π»π are parallelograms. Find the measure of obtuse angle π΄π΅π».

So here we have two parallelograms. We have π΄π΅πΆπ· above the line πΆπΏ and we have πΆπ΅π»π below the line πΆπΏ. In a parallelogram, we can remember that we have two pairs of opposite sides parallel. So π΄π· is parallel to πΆπ΅ and πΆπ΅ is parallel to ππ». In both parallelograms, the opposite sides are also parallel. Weβre asked to find the measure of angle π΄π΅π». And as weβre told that itβs the obtuse angle, an angle weβre looking for is here in orange.

In order to find the obtuse angle π΄π΅π», we can start by finding the reflex angle of π΄π΅π» using what we know about the angles in a parallelogram. We can recall that opposite angles in a parallelogram are equal. So letβs focus on π΄π΅πΆπ·. If opposite angles are equal, then the angle at πΆ will also be 72 degrees. Using the fact that the angles in a quadrilateral add up to 360 degrees means that we can also find the measurements of π΅ and π·. We subtract two lots of 72 degrees from 360 degrees, which gives us 216 degrees. Since we know that opposite angles π΅ and π· are equal in size, then we have 216 degrees, giving us 108 degrees for each of these angles.

Letβs take our second parallelogram πΆπ΅π»π. Once again, we know that opposite angles are equal. And the angle opposite to πΆ is π», meaning that this must also be 51 degrees. Subtracting these two angles from 360 degrees tells us that the sum of angle π΅ and angle π is 258 degrees. And so the angle at π΅, or more specifically angle πΆπ΅π», is 129 degrees. Finally, we can find this obtuse angle of π΄π΅π» by using the fact that the angles about a point sum to 360 degrees. Therefore, the obtuse angle π΄π΅π» is equal to 360 degrees subtract 108 degrees subtract 129 degrees. Evaluating this gives us the answer that the obtuse angle π΄π΅π» is 123 degrees.