To find the measure of angle ∠FDG, we can use the inscribed angle theorem, which states that the measure of an inscribed angle is half the measure of the arc that it intercepts.
In this case, arc \( mFG \) measures \( 60 \) degrees. The angle \( ∠FDG \) intercepts this arc.
According to the inscribed angle theorem:
\[ m∠FDG = \frac{1}{2} mFG \]
Substituting the value of the arc:
\[ m∠FDG = \frac{1}{2} \times 60^\circ = 30^\circ \]
Therefore, the measure of \( ∠FDG \) is \( 30 \) degrees.
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