Question

what is ( mangle f )?
write your answer as an integer or decimal.
( mangle f=square^{circ} )

Explanation:

Step1: Recall the inscribed - angle and central - angle relationship

The measure of an inscribed angle is half the measure of the central angle subtended by the same arc. Let the inscribed angle be \(\angle I\) and the central angle be \(\angle F\). The formula is \(m\angle I=\frac{1}{2}m\angle F\).

Step2: Solve for \(m\angle F\)

Given \(m\angle I = 46^{\circ}\). From the formula \(m\angle F=2\times m\angle I\). Substitute \(m\angle I = 46^{\circ}\) into the formula: \(m\angle F=2\times46^{\circ}\).

Answer:

\(92\)