Question

what is ( mangle efg )?
write your answer as an integer or decimal.
( mangle efg=) (circ)

Explanation:

Step1: Identify the central angle and inscribed angle relationship

The central angle \( \angle EHG = 84^\circ \), and \( \angle EFG \) is an inscribed angle that subtends the same arc \( EG \) as the central angle. The measure of an inscribed angle is half the measure of its subtended central angle.

Step2: Calculate the measure of \( \angle EFG \)

Using the formula for inscribed angles, \( m\angle EFG=\frac{1}{2}m\angle EHG \). Substituting \( m\angle EHG = 84^\circ \), we get \( m\angle EFG=\frac{84^\circ}{2}=42^\circ \).

Answer:

\( 42 \)