Question

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in the figure, $overrightarrow{yx}$ is a tangent to circle o at point x.
$m\overarc{xb} = 52^\circ$
$m\overarc{xa} = 104^\circ$
what is the measure of $\angle xya$
enter your answer in the box.

Explanation:

Step1: Recall the tangent - secant angle theorem

The measure of an angle formed by a tangent and a secant drawn from a point outside the circle is half the difference of the measures of the intercepted arcs. The formula is \(m\angle XYA=\frac{1}{2}(m\widehat{XA}-m\widehat{XB})\).

Step2: Substitute the given values

We know that \(m\widehat{XA} = 104^{\circ}\) and \(m\widehat{XB}=52^{\circ}\). Substitute these values into the formula:
\(m\angle XYA=\frac{1}{2}(104^{\circ}- 52^{\circ})\)

Step3: Calculate the difference inside the parentheses

First, calculate \(104^{\circ}-52^{\circ}=52^{\circ}\).

Step4: Calculate the final angle measure

Then, \(\frac{1}{2}\times52^{\circ} = 26^{\circ}\).

Answer:

\(26^{\circ}\)