what is the value of x?
enter your answer in the box.

it be preferred if i know how you got the answer as well because i really do want to understand this.

VK = VY+YK by the segment addition postulate. Basically adding two segments along a straight line forms a longer segment. In this case, VY and YK combine to form VK

Since VK = x and VY = 22, this means...
VK = VY+YK 
x = 22+YK 
x-22 = YK
YK = x-22



Notice the arc marks where the point T is located. These markings tell us that the two angles VTY and YTK are congruent angles. Because of this, we can use the angle bisector theorem which says that the ratio of the corresponding sides are congruent.

In short, we can form this ratio
VT/VY = KT/KY
which is the ratio of the side adjacent to the angle, to the side opposite the angle

Plug in the given values and solve for x
VT/VY = KT/KY
77/22 = 87.5/(x-22)
77(x-22) = 22*87.5
77(x-22) = 1925
77x-77*22 = 1925
77x-1694 = 1925
77x = 1925+1694
77x = 3619
x = 3619/77
x = 47

47