Question

in circle d with the measure of minor arc \\( \overparen{c e}=30^{\circ} \\), find \\( m \angle c f e \\).

Explanation:

Step1: Use the inscribed - angle theorem

The inscribed - angle theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.
For an inscribed angle \(\angle CFE\) and its intercepted arc \(\overset{\frown}{CE}\), the formula is \(m\angle CFE=\frac{1}{2}m\overset{\frown}{CE}\).

Step2: Substitute the value of the arc measure

Given \(m\overset{\frown}{CE} = 30^{\circ}\), substitute it into the formula: \(m\angle CFE=\frac{1}{2}\times30^{\circ}\).

Answer:

\(15\)