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.
Because we’re told that 𝐴𝐵𝐶𝐷 is
a parallelogram, this means we can say that the line 𝐷𝐶 is parallel to the line
𝐴𝐵 and the line 𝐴𝐷 is parallel to the line 𝐵𝐶. We’re given the two angle
measurements of 𝐵𝐸𝐶 and 𝐸𝐶𝐵, and we’re asked to find this angle 𝐸𝐴𝐷. In order to work out this angle
measurement, we’ll need to remember some of the properties of the angles in
parallelograms.
Firstly, we can remember that
opposite angles are equal, and we could also remember that the sum of two adjacent
angles is 180 degrees. In this parallelogram, the angle
that’s opposite to 𝐴 will be the angle 𝐶. However, we don’t know this total
angle 𝐷𝐶𝐵. We only know that 𝐸𝐶𝐵 is 56
degrees. If we look at our second property,
if we found the angle measurement of 𝐵, then that would help us to work out 𝐴. So how can we find the measurement
of angle 𝐵?
As well as being part of a
parallelogram, this angle at 𝐵 is also part of a triangle. We know that the angles in a
triangle add up to 180 degrees. So this angle of 𝐶𝐵𝐸 is equal to
180 degrees subtract 79 degrees subtract 56 degrees. 180 subtract 79 gives us 101
degrees, and subtracting 56 from that gives us 45 degrees. Remember that this is not our
answer as we still need to work out the angle 𝐸𝐴𝐷. Using the property that the sum of
two adjacent angles is 180 degrees, then we calculate 180 subtract 45 degrees,
giving us our answer of 135 degrees.
