Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

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The **vertex angles** of a kite are the angles formed by two congruent sides.

The **non-vertex angles** are the angles formed by two sides that are not congruent. The two non-vertex angles are always congruent.

Using these facts about the diagonals of a kite (such as how the diagonal bisects the vertex angles) and various properties of triangles, such as the triangle angle sum theorem or Corresponding Parts of Congruent Triangles are Congruent (CPCTC), it is possible to solve for the values of the two vertex angles.

We can use what we know about kite angle properties to find these two missing angles x and y. To start off with let’s look at 120 degrees and x. These two angles if I look on my diagram here are my non vertex angles which are always congruent.

So I know that x and 120 must be congruent so I’m going to erase x and I’m going to write in 120 degrees. So now I got two options one I can use the fact that these four angles must sum to 360 degrees or what I could do is I could draw in a diagonal here, thereby bisecting this angle into two congruent 30 degree angles and I know that y is going to be bisected here. So these angles right here which are congruent will be half of y.

So I see that I've got 120 plus 30 which is 150, which means this angle right here must be 30 degrees. Therefore this angle is 30 degrees. So if I add these up, y must be 60 degrees. The theory of that or the fact that these four angles sum to 360 degrees would also have gotten you know the correct answer. But I think it’s a little shorter to realize that this diagonal bisects these two vertex angles.