# Question Video: Finding the Measure of an Unknown Angle Using the Properties of Parallelograms Mathematics

In the figure, π΄π΅πΆπ· and πΆπ΅π»π are parallelograms. Find πβ π΄π΅π».

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### Video Transcript

In the figure, π΄π΅πΆπ· and πΆπ΅π»π are parallelograms. Find the measure of angle π΄π΅π».

In this question, we are told that the two quadrilaterals formed here are parallelograms, which we can recall are defined as quadrilaterals with both pairs of opposite sides parallel. That would mean that the line segments π΄π· and π΅πΆ are parallel and line segments π΅πΆ and ππ» are parallel. So, we have three parallel line segments here. The other pair of opposite sides in π΄π΅πΆπ·, thatβs line segments π·πΆ and π΄π΅, are parallel. And then in parallelogram πΆπ΅π»π, line segments πΆπ and π΅π» are parallel.

Now, we are asked to find the measure of angle π΄π΅π». And so, recalling some of the angle properties of parallelograms will be helpful here. Firstly, we have that in a parallelogram, opposite angles are equal in measure. And the sum of any two consecutive interior angles is 180 degrees. So, letβs consider that we are given the measure of angle π·π΄π΅. Angle π΄π΅πΆ would be a consecutive interior angle to angle π·π΄π΅. So, the sum of their measures is 180 degrees.

Filling in the information that the measure of angle π·π΄π΅ is 72 degrees, we have that 72 degrees plus the measure of angle π΄π΅πΆ is 180 degrees. And by subtracting 72 degrees from both sides, we have that the measure of angle π΄π΅πΆ is 108 degrees.

Next, knowing the measure of angle πΆπ΅π» would be useful in helping us work out the required angle measure. We can identify that in parallelogram πΆπ΅π»π one of the consecutive interior angles to angle πΆπ΅π» is angle π΅πΆπ, whose measure we are given. Therefore, using the same property as before, we know that these two angle measures must sum to 180 degrees. Filling in the measure of angle π΅πΆπ as 51 degrees, we can determine that the measure of angle πΆπ΅π» is 129 degrees.

Now, we can consider the three angle measures about the point π΅. We can recall that the sum of the angle measures about a point is 360 degrees. So, the sum of the angle measures of 108 degrees, 129 degrees, and the measure of angle π΄π΅π» is 360 degrees. We can simplify the left-hand side to give 237 degrees plus the measure of angle π΄π΅π» equals 360 degrees. And subtracting 237 degrees from both sides, we have the answer that the measure of angle π΄π΅π» is 123 degrees.