Answer: y = 13
Step-by-step explanation:
The tickmarks tell us that sides HG and FG are the same length. The triangle is isosceles. Directly from this, we know that the opposite angles F and H are congruent. Both are 4y-7 degrees.
Angle G is 90 degrees because of Thales' Theorem. This is because HF is the diameter of the circle. It's also the hypotenuse of the right triangle.
For any triangle, the three interior angles always add to 180 degrees.
F+G+H = 180
(4y-7) + (90) + (4y-7) = 180
8y + 76 = 180
8y = 180-76
8y = 104
y = 104/8
y = 13