Question Video: Finding the Measure of an Unknown Angle Using the Properties of Parallelograms | Nagwa Question Video: Finding the Measure of an Unknown Angle Using the Properties of Parallelograms | Nagwa

# 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 the measure of obtuse angle 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 obtuse angle π΄π΅π».

So here we have two parallelograms. We have π΄π΅πΆπ· above the line πΆπΏ and we have πΆπ΅π»π below the line πΆπΏ. In a parallelogram, we can remember that we have two pairs of opposite sides parallel. So π΄π· is parallel to πΆπ΅ and πΆπ΅ is parallel to ππ». In both parallelograms, the opposite sides are also parallel. Weβre asked to find the measure of angle π΄π΅π». And as weβre told that itβs the obtuse angle, an angle weβre 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 letβs focus on π΄π΅πΆπ·. If opposite angles are equal, then the angle at πΆ 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.

Letβs take our second parallelogram πΆπ΅π»π. Once again, we know that opposite angles are equal. And the angle opposite to πΆ 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 πΆπ΅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.

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