Question

Which statements about the arcs and angles are true? select three options. ∠efd ≅ ∠egd ∠egd ≅ ∠ecd arc e d is-congruent-to arc f d marc e f = 60° marc f d = 120°

Answer 1

The true statements about the arcs and angles in circle C are:

1. ∠EFD ≅ ∠EGD.
2. Arc ED ≅ arc FD.
3. m arc FD = 120°.

How to analyze the arcs and angles?

In Geometry, the sum of the measures of the interior angles in a quadrilateral is equal to 360°. Thus, we have:

m∠G + m∠GDC + m∠DCE + m∠GEC = 360°

60 + 90 + m∠DCE + 90 = 360

240 + m∠DCE = 360

m∠DCE = 360 - 240

m∠DCE = 120°.

Since ∠DFE is an inscribed angle that is subtended by arc DE, we have:

m∠DFE =  m∠DCE

m∠DFE =  120

m∠DFE = 1/2 × 120

m∠DFE = 60°.

Therefore, ∠EFD ≅ ∠EGD.

From circle C, we can deduce that side ED is subtended by arc ED and side FD is subtended by arc FD (side ED ≅ side FD). Thus, arc ED ≅ arc FD and m arc FD is equal to 120°.

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