Question

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° What is the measure of Arc J M? 77° 90° 132° 154°

Answer 1

Answer:

The measure of Arc EH is 123°.

Step-by-step explanation:

Consider the diagram below.

It is provided that ∠EDH ≅ ∠EDG.

This implies that: ∠EDH = ∠EDG

The arc measure is same as the measure of the central angle.

That is:

arc FE = ∠EDF = 57°

arc FG = ∠FDG = 66°

Compute the measure of angle ∠EDH as follows:

arc EH = ∠EDH

           =∠EDG

           = ∠EDF + ∠FDG

           = 57° + 66°

           = 123°

Thus, the measure of Arc EH is 123°.