Video Transcript
Given that 𝐴𝐵𝐶𝐷 is a
parallelogram and the measure of angle 𝐶 equals 68 degrees, find the measure of
angle 𝐴.
So, here we have a
parallelogram. We might recall some facts about
the sides in a parallelogram. For example, it has two pairs of
parallel sides, and each of these opposite sides are also congruent. But what should we know about the
angles in a parallelogram? We should remember that opposite
angles are equal or congruent.
We could say that in our
parallelogram that angle 𝐷 is equal to angle 𝐵. We can also say that angle 𝐴 is
equal to angle 𝐶. We’re given in the question that
the measure of angle 𝐶 is 68 degrees. So that means that the measure of
angle 𝐴 is also 68 degrees. And therefore, we’ve answered the
question to find the measure of angle 𝐴.
It’s interesting to note that when
we have a parallelogram, we only need to have one angle in order to work out all the
other angles. For example, in our parallelogram,
we have the measure of angle 𝐴 and 𝐶 are both 68 degrees. We can remember that in any
quadrilateral, the angles sum to 360 degrees. So, we could work out that in our
parallelogram, the angles at 𝐷 and 𝐵 must add up to 224 degrees. Since we have opposite angles
equal, then we know that 𝐷 and 𝐵 must be half of 224. So, they would both be 112
degrees. But here, we were just asked for
the measure of angle 𝐴, which is 68 degrees.
