Question

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chords and arcs
what is the measure of $widehat{dg}$?
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$square^circ$

Explanation:

Step1: Identify inscribed angle rule

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Calculate arc measure

Let $m\overset{\frown}{DG}$ be the measure of arc $DG$. The inscribed angle $\angle DHG = 55^\circ$, so:
$$m\overset{\frown}{DG} = 2 \times m\angle DHG$$
$$m\overset{\frown}{DG} = 2 \times 55^\circ = 110^\circ$$

Answer:

$110$