Circle D is shown. Line segments D E, D F, D G, and D H are radii. Angle E D F is 55 degrees, angle F D G is 70 degrees, and angle G D H is 110 degrees.
Which arc is congruent to Arc E H?

Arc G H
Arc F H
Arc G E
Arc F G

The figure is missing but we can solve the problem from the given information

Arc GE is congruent to arc EH ⇒ 3rd answer

Step-by-step explanation:

In a circle

Look to the attached figure

In circle D

∵ D is the center of the circle

∵ DE and DF are radii

∴ ∠EDF is an central angle subtended by arc EF

- The measure of the central angle is equal to the measure

   of its subtended arc

∴ m∠EDF = m of arc EF

∵ m∠EDF = 55°

∴ m of arc EF = 55°

∵ DF and DG are radii

∴ ∠FDG is an central angle subtended by arc FG

∴ m∠FDG = m of arc FG

∵ m∠FDG = 70°

∴ m of arc FG = 70°

∵ DG and DH are radii

∴ ∠GDH is an central angle subtended by arc GH

∴ m∠GDH = m of arc GH

∵ m∠GDH = 110°

∴ m of arc GH = 110°

∵ The measure of the circle = 360°

- The circle divided into 4 arcs EF, FG, GH and HE

∴ m arc EF + m arc FG + m arc GH + m arc HE = 360°

- Substitute the measures of arcs EF, FG and GH

∴ 55 + 70 + 110 + m arc HE = 360

∴ 235 + m arc HE = 360

- Subtract 235 from both sides

∴ m arc HE = 125°

∵ m of arc GE = m of arc EF + m of arc FG

∵ m of arc EF = 55°

∵ m of arc FG = 70°

∴ m of arc GE = 55 + 70 = 125°

∴ m of arc GE = m of arc EH

Arc GE is congruent to arc EH

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step-by-step explanation:

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