Answer
$H$
Work Step by Step
The angle bisector theorem states that a point that is located on an angle's bisector is equidistant from the angle's sides.
In this diagram, we see that a ray is the angle bisector of an angle. We also see a point that is on the angle bisector. Therefore, we know that this point is equidistant from each side of the angle. Let us set the distance from the point to one side of the angle equal to the distance of the point from the other side of the angle:
$2y = 5y - 7$
$-3y = -7$
$y = \frac{7}{3}$
This answer corresponds to option $H$.
