The figure of the kite shown in the figure is a quadrilateral because it has four sides. The lengths of each side is expressed as a function of x and y. In order to determine the values of x and y, you make use of the short lines that mark the sides. These are symbols of congruency. If two sides are equal, you mark them both with the same symbol. So for the figure above, side NM = side LM and side KL = side KN. Therefore, we equate them as follows:
NM = LM
2x + 6 = 3x - 1
3x - 2x = 6 +1
x = 7
KL = KN
2y + 5 = y + 10
2y-y = 10 - 5
y = 5
So, we know that the values are x=7 and y=5. We use this to know the actual values of sides KN and NM.
KN = y + 10
KN = 5 + 10
KN = 15
NM = 2x + 6
NM = 2(7) + 6
NM = 20
