Finding The Measure Of An Angle In A Parallelogram Given ... - Nagwa

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.