Question

Given: WZ is perpendicular to VY, WZ bisects VY, VZ = 2x+2, and ZY = 3x-4

Answer 1

The measure of VY is 28 units

Solution:

To find: The measure of VY

From the given,

WZ bisects VY, then  we can conclude that VZ  =  ZY  ---> (1)

VZ=2x+2 and ZY=3x-4

Substituting the above values in (1) we get,

$2x+2=3x-4\rightarrow2x-3x=-4-2$

$\Rightarrow-1x=-6\rightarrow-x=-6$

$\Rightarrow x=6$

Since, WZ bisects VY, VY=VZ+ZY ---> (2)

On substituting the value of x in (2) we get,

$VY=(2x+2)+(3x-4)=(2\times6+2)+(3\times6-4)$

$VY=(12+2)+(18-4)\rightarrow VY=(14)+(14)$

$\Rightarrow VY=28 \text{ units }$