Questions: What is the measure of arc EF in circle H? 41° 50° 114° 173°

Solution Steps

The problem provides two angles: ∠DEF = 123° and ∠DGE = 73°.

In a circle, the measure of an arc is twice the measure of the inscribed angle that subtends the arc. Here, ∠DEF is an inscribed angle that subtends arc EF.

Since ∠DEF = 123°, the measure of arc EF is twice this angle: \[ \text{Measure of arc EF} = 2 \times 123° = 246° \]

A circle has 360°. Since arc EF is 246°, the remaining arc (arc DGF) is: \[ 360° - 246° = 114° \]

Final Answer