find the value of each variable. the dot represents the center of the circle. lines that appear tangent are…

Explanation:

Step1: Identify the measure of the intercepted arc for angle $a$

Angle $a$ is an inscribed angle. Its measure is half the measure of its intercepted arc, which is $58^{\circ}$. $$a = \frac{1}{2} \cdot 58^{\circ}$$

Step2: Calculate the value of $a$

$$a = 29^{\circ}$$

Step3: Identify the measure of the intercepted arc for angle $b$

Angle $b$ is formed by a tangent and a chord. Its measure is half the measure of the intercepted arc, which is $58^{\circ}$. $$b = \frac{1}{2} \cdot 58^{\circ}$$

Step4: Calculate the value of $b$

$$b = 29^{\circ}$$

Step5: Identify the measure of the intercepted arc for angle $c$

Angle $c$ is an inscribed angle. Its measure is half the measure of its intercepted arc, which is $82^{\circ}$. $$c = \frac{1}{2} \cdot 82^{\circ}$$

Step6: Calculate the value of $c$

$$c = 41^{\circ}$$

Answer:

$a = 29$ $b = 29$ $c = 41$