To determine the value of [tex]\( x \)[/tex] that makes quadrilateral [tex]\( WXYZ \)[/tex] a parallelogram, given the equations [tex]\( WC = 2x + 5 \)[/tex] and [tex]\( CY = 3x + 2 \)[/tex], we need to understand one fundamental property of parallelograms: opposite sides are equal.
In our problem, the segments [tex]\( WC \)[/tex] and [tex]\( CY \)[/tex] are opposite sides of the parallelogram. Therefore, we set their lengths equal to each other to form an equation and find [tex]\( x \)[/tex].
1. Set the expressions for the sides equal to each other:
[tex]\[
2x + 5 = 3x + 2
\][/tex]
2. Next, we need to isolate [tex]\( x \)[/tex]. First, subtract [tex]\( 2x \)[/tex] from both sides of the equation to eliminate [tex]\( x \)[/tex] from the left side:
[tex]\[
5 = x + 2
\][/tex]
3. Finally, subtract 2 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
5 - 2 = x
\][/tex]
[tex]\[
x = 3
\][/tex]
So, for quadrilateral [tex]\( WXYZ \)[/tex] to be a parallelogram, [tex]\( x \)[/tex] must equal [tex]\( 3 \)[/tex].
