Question

Find the value of each variable. The dot represents the center of the circle Lines that appeartangent are tangent.

Answer 1

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:

`\begin{gathered} a=(1)/(2)(50) \\ \\ a=25 \end{gathered}`

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°:

`\begin{gathered} a+b=90 \\ b=90-a \\ b=90-25 \\ b=65 \end{gathered}`

Angle c is an inscribed angle and the intercepted arc is 82°. Then, the measure of angle c is:

`\begin{gathered} c=(1)/(2)(82) \\ \\ c=41 \end{gathered}`

Then, you have the next values for the variables:

a=25°

b=65°

c=41°