A)
modifying 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)
Responses
96°
96°
128°
128°
26°
26°
58°
To find the measure of angle YAC, we can use the fact that the angle at the center of a circle is twice the angle at the circumference that subtends the same arc. Since the arc BY is 64°, the angle at the center of the circle (angle BOY) is 2*64 = 128°.
Angle YAC is opposite angle BOY within triangle BYA since they share segment YA.
Therefore, angle YAC = 180 - 128 = 52°.
Therefore, the correct answer is:
26°.