Question

in circle e with the measure of arc df = 90°, find m∠def.
circle e with center e, points d and f on the circle, and segment ed and ef drawn

Explanation:

Step1: Recall central angle theorem

The measure of a central angle is equal to the measure of its intercepted arc. In circle \( E \), \( \angle DEF \) is a central angle that intercepts arc \( DF \).

Step2: Apply the theorem

Given \( m\overset{\frown}{DF} = 90^\circ \), by the central angle theorem, \( m\angle DEF=m\overset{\frown}{DF} \).

Answer:

\( 90^\circ \)