Ac is tangent to circle o at a. if mby= 64 degrees, what is myac?

The correct answer is ∠YAC measures 58 degrees.

Please see the attached picture.

A line tangent to a circle is perpendicular to the diameter passing by the tangent point.

Therefore, we can say that ∠BAC = 90°

We also can infer from the picture that ∠BAC = ∠BAY + ∠YAC

Solve for ∠YAC:
∠YAC = ∠BAC - ∠BAY

We also know that the angle at the center (∠BOY) is twice the angle at the circumference (∠BAY), therefore:
∠BAY = (1/2) · mBY
           = 0.5 · 64 
           = 32°

Now, substitute the values in the formula for ∠YAC:
∠YAC = ∠BAC - ∠BAY
           = 90 - 32
           = 58°

Hence, ∠YAC measures 58°.