Question

what is the measure of \\( \angle c \\)?

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Apply the theorem

Here, the intercepted arc of \(\angle C\) is arc \(AB\) which has a measure of \(76^{\circ}\). Let \(m\angle C = x\). By the inscribed - angle theorem \(x=\frac{1}{2}\times\) (measure of arc \(AB\)).
So \(x = \frac{76^{\circ}}{2}\)

Answer:

\(38^{\circ}\)