Question

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Explanation:

Step1: Find the measure of arc \(ACB\)

The total measure of a circle is \(360^{\circ}\). Given two arcs \(83^{\circ}\) and \(115^{\circ}\), the measure of arc \(ACB\) is \(360^{\circ}-83^{\circ}-115^{\circ}=162^{\circ}\)

Step2: Use the inscribed - angle formula

The measure of an inscribed angle is half the measure of its intercepted arc. Let the unknown angle be \(x\). The intercepted arc of angle \(x\) is arc \(ACB\) which is \(162^{\circ}\). So \(x = \frac{1}{2}\times162^{\circ}\)

Answer:

\(81^{\circ}\)