Question Video: Finding the Measure of an Angle in a Parallelogram given the Other Three Angles’ Measures Mathematics

Video Transcript

𝐴𝐵𝐶𝐷 is a parallelogram in which the measure of angle 𝐵𝐸𝐶 equals 79 degrees and the measure of angle 𝐸𝐶𝐵 equals 56 degrees. Determine the measure of angle 𝐸𝐴𝐷.

In this figure, we can see that we have the two angles 𝐵𝐸𝐶 and 𝐸𝐶𝐵 given. And we need to determine the measure of angle 𝐸𝐴𝐷. 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 𝐸𝐴𝐷, then a consecutive angle which might be useful to know is the measure of angle 𝐶𝐵𝐸. If we knew this, then by the second property here we could calculate the measure of angle 𝐸𝐴𝐷.

Let’s consider this triangle 𝐵𝐸𝐶. 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 𝐶𝐵𝐸 plus 56 degrees plus 79 degrees is equal to 180 degrees. Rearranging this, we obtain that the measure of angle 𝐶𝐵𝐸 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 𝐸𝐴𝐷 and the measure of angle 𝐶𝐵𝐸 must add to be 180 degrees. To find the measure of angle 𝐸𝐴𝐷 then, we subtract 45 degrees from 180 degrees, giving us an answer of 135 degrees.