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Find the value of each variable. For each circle, the dot is the center

Find the value of each variable. For each circle, the dot is the center-example-1
User Davey Chu
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1 Answer

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We have to use the theorem about the angles formed by two intersecting chords.


\begin{gathered} x=(1)/(2)(60+108) \\ x=(1)/(2)\cdot168=84 \end{gathered}

Then, we find the supplement of x, which is c.


\begin{gathered} x+c=180 \\ c=180-x \\ c=180-84 \\ c=96 \end{gathered}

Angle c measures 96°.

Then, we use the inscribed angle theorem to find b


b=(1)/(2)\cdot60=30

At last, we use the interior angles theorem to find a


\begin{gathered} a+b+c=180 \\ a+30+96=180 \\ a=180-96-30=54 \end{gathered}

Hence, a, b, and c are equal to 54°, 30°, and 96°, respectively.

User Smontanaro
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