Answer:
[tex]\begin{gathered} a=128^{\circ} \\ b=150^{\circ} \\ c=41^{\circ} \end{gathered}[/tex]Explanation:
Given the figure in the attached image.
We want to solve for a,b and c;
From the Geometry of circles, the inscribed angle is half the angle on the intercepted arc;
[tex]\text{Inscribed angle=}\frac{1}{2}angle\text{ on the intercepted arc}[/tex]So, we have;
[tex]\begin{gathered} c=\frac{82^{\circ}}{2} \\ c=41^{\circ} \end{gathered}[/tex]And;
[tex]\begin{gathered} a=2(64^{\circ}) \\ a=128^{\circ} \end{gathered}[/tex]For b, the total angle of the circle circumference is 360 degrees;
[tex]\begin{gathered} a+82^{\circ}+b=360^{\circ} \\ b=360^{\circ}-(82^{\circ}+a) \\ b=360^{\circ}-(82^{\circ}+128^{\circ}) \\ b=360^{\circ}-(210^{\circ}) \\ b=150^{\circ} \end{gathered}[/tex]Therefore, we have;
[tex]\begin{gathered} a=128^{\circ} \\ b=150^{\circ} \\ c=41^{\circ} \end{gathered}[/tex]