in the diagram of circle a, what is the measure of \$\\angle xyz\$? \…

QUESTION IMAGE

$in the diagram of circle a, what is the measure of \$\\angle xyz\$? \…$

Question

in the diagram of circle a, what is the measure of \$\angle xyz\$?

\$35^\circ\$
\$70^\circ\$
\$75^\circ\$
\$140^\circ\$

Explanation:

Response

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Calculate the measure of the remaining arc WX

\[
m\widehat{WX} = 360^\circ - 175^\circ - 105^\circ = 80^\circ
\]

Determine the measure of the intercepted arc XZ

\[
m\widehat{XZ} = 105^\circ
\]

Apply the intersecting secant-tangent angle formula

\[
m\angle XYZ = \frac{m\widehat{WXZ} - m\widehat{XZ}}{2} = \frac{(80^\circ + 175^\circ) - 105^\circ}{2} = \frac{255^\circ - 105^\circ}{2} = 75^\circ
\]
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Answer: