There are a couple of key facts about kites that will help you solve problems when you have missing sides or missing angles.
The first key part about how to identify a kite is you have two pairs of consecutive congruent sides. Not opposite like in a parallelogram or a rectangle. Notice, we have two consecutive sides here and they're both congruent. But these two sides are not congruent to this pair. That's the first key thing about a kite.
The second key thing is the nonvertex angles are congruent. So if you want to call this angle a vertex angle, and this angle a vertex angle, then these two non-vertex angles will always be congruent.
The third key thing is that the diagonals are perpendicular. So if I drew in a diagonal between the vertices and between the nonvertex angles, these two will intersect at a 90-degree angle.
Another key fact about this is that this diagonal between the two non-vertex angles is bisected by this longer diagonal. So a couple key things to remember when you are trying to solve problems that involve a kite.
And one other thing that I forgot to mention is that this vertex angle is bisected by this diagonal. This vertex angle is also bisected but not necessarily congruent to this angle.
So a lot going on in a kite. We've got diagonals that are perpendicular to each other. This diagonal was bisected, the angles in the vertex are bisected, and we've got two pairs of consecutive congruent sides.