Question

1. find x.

Explanation:

Step1: Use the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Let the measure of the arc \(x\) be the arc intercepted by the inscribed angle of \(30^{\circ}\).

Step2: Set up the equation

We know that the formula is \(m\angle=\frac{1}{2}m\overset{\frown}{arc}\). Given \(m\angle = 30^{\circ}\), then \(30^{\circ}=\frac{1}{2}x\).

Step3: Solve for \(x\)

Multiply both sides of the equation \(30^{\circ}=\frac{1}{2}x\) by \(2\). So \(x = 2\times30^{\circ}\).

Answer:

\(x = 60^{\circ}\)