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HandyGandy · Answer 1 · 2023-08-05T07:34:17+0000

Answer:

$\begin{gathered} x=\text{ 25\degree} \\ y=\text{ 102.5\degree} \end{gathered}$

Explanation:

For an angle formed outside of a circle by an intersection of a tangent and a secant, we can state that:

$\text{ Angle formed by tangent and secant=1/2\lparen difference of intercepted arcs\rparen}$

Then, to find x:

$\begin{gathered} mNow, to find ''y'', by the theorem of an angle formed by a chord and a tangent, take half of the arc CD. Since the full circle is 360 degrees, subtract the given arc and the resulting arc ''x'' from above:[tex]\begin{gathered} y=(mCD)/(2) \\ mCD=360-130-25 \\ mCD=205\text{ degrees} \\ \\ y=(205)/(2) \\ y=102.5\text{ degrees} \end{gathered}$

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