The measure if an inscribed angle is half the measure of the intercepted arc
Angle a is an inscribed angle and the intercepted arc is 50°. Then, the measure of angle a is:
[tex]\begin{gathered} a=\frac{1}{2}(50) \\ \\ a=25 \end{gathered}[/tex]
Line m is tangent, then it is perpendicular to the diameter of the circle. It forms a angle of 90° with the diameter of the circle.
The sum of angles a and b is 90°:
[tex]\begin{gathered} a+b=90 \\ b=90-a \\ b=90-25 \\ b=65 \end{gathered}[/tex]
Angle c is an inscribed angle and the intercepted arc is 82°. Then, the measure of angle c is:
[tex]\begin{gathered} c=\frac{1}{2}(82) \\ \\ c=41 \end{gathered}[/tex]
Then, you have the next values for the variables:
a=25°
b=65°
c=41°
