Check the picture below.
on 8), both angles are inscribed in the circle, and both are intercepting the same arc, thus they must be the same angle value.
on 9), the inscribed angle theorem refers to the angle of the intercepted arc, and the arc gets its angle value from the central angle, on this case, the central angle for the red arc is 64°, so the inscribed angle intercepting it, must be half that.
