Question

ok so i had gotten 75 for this and they said its incorrect i did 68 = 1/2(x + 61)

Answer 1

You misunderstood the theorem which is that the angle BETWEEN the chords is half of the subtended arcs which tells you instead that the arc subtended by 61 degrees is given by

(68 + itsarc)/2 = 61 so the arc is 54.

The chord of that arc would subtend 54 at the center and another theorem tells you that an angle subtended on the circumference is half that at the center, or 27.

Think that's right, someone check.