# Question Video: Finding the Measure of an Angle in a Parallelogram given the Other Three Anglesβ Measures Mathematics

π΄π΅πΆπ· is a parallelogram in which πβ π΅πΈπΆ = 79Β° and πβ πΈπΆπ΅ = 56Β°. Determine πβ πΈπ΄π·.

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### Video Transcript

π΄π΅πΆπ· is a parallelogram in which the measure of angle π΅πΈπΆ equals 79 degrees and the measure of angle πΈπΆπ΅ equals 56 degrees. Determine the measure of angle πΈπ΄π·.

In this figure, we can see that we have the two angles π΅πΈπΆ and πΈπΆπ΅ given. And we need to determine the measure of angle πΈπ΄π·. As we are told that this is a parallelogram, then that means that we can apply the properties of parallelograms to help us find this unknown angle. And as we are thinking about an angle, then the two angle properties of a parallelogram are that opposite angles are equal in measure and the sum of the measures of two consecutive angles is 180 degrees. As we want to find the measure of angle πΈπ΄π·, then a consecutive angle which might be useful to know is the measure of angle πΆπ΅πΈ. If we knew this, then by the second property here we could calculate the measure of angle πΈπ΄π·.

Letβs consider this triangle π΅πΈπΆ. As we are given two angles, we can apply the property that the interior angle measures in a triangle sum to 180 degrees. This means that the measure of angle πΆπ΅πΈ plus 56 degrees plus 79 degrees is equal to 180 degrees. Rearranging this, we obtain that the measure of angle πΆπ΅πΈ is equal to 180 degrees subtract 135 degrees, and that is 45 degrees. And then as previously mentioned, we can identify this pair of consecutive angles. The measure of angle πΈπ΄π· and the measure of angle πΆπ΅πΈ must add to be 180 degrees. To find the measure of angle πΈπ΄π· then, we subtract 45 degrees from 180 degrees, giving us an answer of 135 degrees.