Find the values of the variables in this kite.

Solution:

Variables used = x and y

In the kite (figure provided), there are four sides in which two are equal and other two are equal.
Let the longer two sides be a and b & smaller two sides be c and d.
a=b and c=d
Equation for longer two sides which are equal:
2x+5 and x+12

Using above two equations, we find the value of x.
By equating,
2x+5 = x+12
2x-x = 12-5
x = 7

Now equation for smaller two sides are:
y-4 and x+5

x = 7
so, x+5 = 7+5 = 12

Now we need to find value of y. We know c=d (both smaller sides are equal), therefore, if one side is 12 then other should be 12 as well.

12 = y-4
y = 16

x = 7 and y = 16