Question

what is the measure of arc ef in circle h?
41°
50°
114°
173°

Explanation:

Step1: Recall inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. For $\angle DEG = 123^\circ$, its intercepted arc is arc $DGF$. So:
$$\text{Arc } DGF = 2 \times 123^\circ = 246^\circ$$

Step2: Find total circle arc measure

The total measure of arcs in a circle is $360^\circ$. Subtract arc $DGF$ to get arc $DE$:
$$\text{Arc } DE = 360^\circ - 246^\circ = 114^\circ$$

Step3: Calculate arc $EF$

We know arc $DE = 73^\circ$. Subtract this from arc $DF$ to get arc $EF$:
$$\text{Arc } EF = 114^\circ - 73^\circ = 41^\circ$$

Answer:

41°