Question

Find the measure of the arc:the central angle is supplementary to a 20 angle

Answer 1

The measure of the arc is the same as the measure of the central angle, so if we know that the central angle is supplementary to 20 angle, we can find out the central angle and, thus, the measure of the arc.

Actually, the angle of 20 don't say if it is in degrees, but we will have to assume this to go ahead with the question.?

So, assuming the ohrase is "the central angle is supplementary to a 20° angle", let x be the central angle, then, it it is supplementary to 20°, we have that the sum of x and 20° is equal to 180°:

`\begin{gathered} x+20\degree=180\degree \\ x=180\degree-20\degree \\ x=160\degree \end{gathered}`

And since the central angle is the same as the measure of its arc, we have that the measure of the arc is 160°.