Video Transcript
Given that 𝐴𝐵𝐶𝐷 is a kite, the
measure of angle 𝐴 equals 127 degrees and the measure of angle 𝐷 equals 86
degrees. Find the measure of angle 𝐶.
Let’s start this question by
looking at our kite and marking on the angles that we’re being given. Here, we have angle 𝐴 as 127
degrees and angle 𝐷 as 86 degrees. Let’s recall the fact that we might
know about the angles in a kite. And that is that a kite has one set
of congruent opposite angles. We can always find the congruent
opposite angles by thinking about this with the line of symmetry. So here, the two congruent angles
would be angled 𝐷 and angle 𝐵. We can write this as the measure of
angle 𝐵 is equal to the measure of angled 𝐷. So the measure of angle 𝐵 is also
86 degrees.
In the question, we’re asked to
find the measure of angle 𝐶. We have three angles in our
kite. How will we find this missing
angle? Well, we can use the fact that the
angles in a quadrilateral are up to 360 degrees. And since our kite is a
quadrilateral, we can use this to say that the measure of angle 𝐶 is equal to 360
degrees subtract our two 86-degree angles and subtract our other 127-degree angle,
which will give us 61 degrees. Therefore, our final answer is the
measure of angle 𝐶 equals 61 degrees.
