Question

• The circle has points A, B, and C, with line AC tangent to the circle at point O.
• The measure of angle BY is given as 64 degrees.
• The question asks to find the measure of angle YAC.
what’s the answer. 26 degrees , 180 degrees,22 degrees,58 degrees

Answer 1

To find the measure of angle YAC, we can use the properties of tangents and circles.

Since line AC is tangent to the circle at point O, the angle formed between the tangent (line AC) and the radius (line AO) at point O is a right angle (90 degrees).

Given that angle BY is 64 degrees, we can use the fact that the angles formed by a tangent and a chord through the point of tangency (O) are equal. Therefore, angle YAB (the angle formed by the line segment YA and the radius OA) is equal to angle BY, which is 64 degrees.

Now, since triangle YAC has a sum of angles equaling 180 degrees, we have:

\[
\text{Angle YAC} + \text{Angle YAB} + 90^\circ = 180^\circ
\]

Substituting the known value for angle YAB:

\[
\text{Angle YAC} + 64^\circ + 90^\circ = 180^\circ
\]

Combining the known angles:

\[
\text{Angle YAC} + 154^\circ = 180^\circ
\]

Now, we can solve for angle YAC:

\[
\text{Angle YAC} = 180^\circ - 154^\circ = 26^\circ
\]

Thus, the measure of angle YAC is **26 degrees**.