1)YWXZ is a parallelogram with diagonals that intersect at point S. If WS = 10 and SZ = 2x – 6, find x.
f WS = 10 and SZ = 2x – 6, find x.
21
To find the value of x, we need to use the properties of a parallelogram and the intersecting diagonals.
In a parallelogram, the diagonals bisect each other, which means that they divide each other into two equal parts. Therefore, we can say that WS (one half of the diagonal) is equal to SZ (the other half of the diagonal).
Given that WS = 10 and SZ = 2x – 6, we can set up the equation:
WS = SZ
10 = 2x – 6
To solve for x, we need to isolate x on one side of the equation. We can do this by adding 6 to both sides of the equation:
10 + 6 = 2x
16 = 2x
Now, we can divide both sides of the equation by 2 to solve for x:
16/2 = 2x/2
8 = x
Therefore, x = 8.