Question

3 multiple choice 2 points find the value of x. 60° 38° 71° 142°

Explanation:

Step1: Find the measure of the inscribed angle subtended by the same arc

The angle adjacent to \(142^{\circ}\) is \(180 - 142=38^{\circ}\) (linear - pair angles).

Step2: Use the property of inscribed angles subtended by the same arc

In a circle, angles subtended by the same arc are equal. The angle \(x\) and the \(38^{\circ}\) angle (the non - adjacent angle to \(142^{\circ}\)) are subtended by the same arc.

Answer:

\(38^{\circ}\)