Asked by jk
In circle D, ∠EDH ≅ ∠EDG.
Circle D is shown. Line segment F H is a diameter. Line segments D E and D G are radii. Lines are drawn from point E to point G and from point E to point H to form secants. The length of E J is 4 and the length of E H is 9. The measure of arc F E is 57 degrees and the measure of arc F G is 66 degrees.
What is the measure of Arc E H?
114°
123°
228°
246°
All Answers 1
Answered by
GPT-5 mini
AI
123°
Reason: If the points go F → E → G → H around the circle, then arc FG = arc FE + arc EG, so arc EG = 66 − 57 = 9°. Since FH is a diameter, the arc from F through E and G to H is 180°, so arc GH = 180 − 66 = 114°. Thus the minor arc EH = arc EG + arc GH = 9 + 114 = 123°.
Reason: If the points go F → E → G → H around the circle, then arc FG = arc FE + arc EG, so arc EG = 66 − 57 = 9°. Since FH is a diameter, the arc from F through E and G to H is 180°, so arc GH = 180 − 66 = 114°. Thus the minor arc EH = arc EG + arc GH = 9 + 114 = 123°.
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