The figure is missing but we can solve the problem from the given information
Answer:
Arc GE is congruent to arc EH ⇒ 3rd answer
Step-by-step explanation:
In a circle
- The angle whose vertex is the center of the circle and its two sides are radii, is called central angle
- The measure of the central angle is equal to the measure of its subtended arc
- The measure of a circle is 360°
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
