Question Video: Determining the Measure of an Angle in a Kite Using Its Properties Mathematics

Given that 𝐴𝐡𝐢𝐷 is a kite, π‘šβˆ π΄ = 127Β°β€Ž, and π‘šβˆ π· = 86Β°β€Ž, find π‘šβˆ πΆ.


Video Transcript

Given that 𝐴𝐡𝐢𝐷 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 𝐢.

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 𝐡. We can write this as the measure of angle 𝐡 is equal to the measure of angled 𝐷. So the measure of angle 𝐡 is also 86 degrees.

In the question, we’re asked to find the measure of angle 𝐢. 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 𝐢 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 𝐢 equals 61 degrees.

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