Question

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

Answer 1

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

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

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

$b=\frac{1}{2}\cdot60=30$

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.