Question

in the figure, \\( \overrightarrow { y x } \\) is a tangent to circle \\( o \\) at point \\( x \\).
\\( m \overleftrightarrow { x b } = 52 ^ { \circ } \\)
\\( m \overleftrightarrow { x a } = 104 ^ { \circ } \\)
what is the measure of \\( \angle x y a \\)?
enter your answer in the box.

Explanation:

Step1: Recall the formula for the measure of an angle formed by a tangent and a secant

The measure of an angle formed by a tangent and a secant is given by $\frac{1}{2}(m\overarc{XA}-m\overarc{XB})$.

Step2: Substitute the given values

We are given that $m\overarc{XA} = 104^{\circ}$ and $m\overarc{XB}=52^{\circ}$.
Substitute these values into the formula: $\frac{1}{2}(104 - 52)$.

Step3: Calculate the result

First, calculate the value inside the parentheses: $104 - 52=52$.
Then, multiply by $\frac{1}{2}$: $\frac{1}{2}\times52 = 26$.

Answer:

$26^{\circ}$