Question

in circle d, ∠edh ≅ ∠edg. what is the measure of arc eh? 123°, 228°, 114°, 246°

Explanation:

Step1: Recall central - angle arc relationship

The measure of an arc is equal to the measure of its central angle.

Step2: Find the measure of central angle ∠EDH

Since ∠EDH≅∠EDG and we know that the measure of an inscribed - angle ∠FEG = 57°. The central angle ∠FDG that subtends the same arc as ∠FEG is 2×57° = 114°. Also, we know that the measure of arc FG is 66°. Let's focus on the fact that ∠EDH and ∠EDG are equal. The measure of arc EH is related to the central angle ∠EDH. Since the measure of an inscribed - angle that subtends half of the arc, and we know that if we consider the fact that the central angle corresponding to arc EH is composed of two equal angles (because ∠EDH≅∠EDG). If we assume the central angle ∠EDH = x and ∠EDG=x, and we know that the measure of an arc is equal to the measure of its central angle. The measure of arc EH is 2 times the measure of the inscribed - angle that subtends half of arc EH. Given that the inscribed - angle related to half of arc EH is 57°, the central angle ∠EDH + ∠EDG which is the central angle for arc EH is 114°.

Answer:

114°