Questionmodifying above upper A upper C with right pointing arrow is tangent to circle O at A. The diagram is not drawn to scale.A circle is shown with center O and points B, Y, and A. Line BOA is a vertical line that runs through the center of the circle. Line YA is a diagonal line that runs through the right half of the circle. Line AC extends out from the circle.If measure of modifying above Upper B Upper Y with arc= 64°, what is measure of angle Y A C?(1 point)Responses96°96°128°128°26°26°58°

Question

Questionmodifying above upper A upper C with right pointing arrow is tangent to circle O at A. The diagram is not drawn to scale.A circle is shown with center O and points B, Y, and A. Line BOA is a vertical line that runs through the center of the circle. Line YA is a diagonal line that runs through the right half of the circle. Line AC extends out from the circle.If measure of modifying above Upper B Upper Y with arc= 64°, what is measure of angle Y A C?(1 point)Responses96°96°128°128°26°26°58°

Answer 1

To find the measure of angle YAC, we need to first find the measure of angle BOY.

Since angle BOY is an inscribed angle, its measure is half the measure of its intercepted arc.

Therefore, angle BOY = 64° / 2 = 32°.

Now, angle BOA is a right angle, so angle BOY + angle YAC = 90°.

Therefore, angle YAC = 90° - angle BOY = 90° - 32° = 58°.

So, the measure of angle YAC is 58°.

Therefore, the correct answer is:

58°