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In the diagram, EFGH is a cyclic quadrilateral in which EH || FG, EG and FH are ...


Question

In the diagram, EFGH is a cyclic quadrilateral in which EH || FG, EG and FH are chords. If < FHG = 424\(^{\circ}\) and < EFH = 34\(^{\circ}\)

Options

A) 34\(^{\circ}\)

B) 42\(^{\circ}\)

C) 52\(^{\circ}\)

D) 76\(^{\circ}\)

The correct answer is C.

Explanation:

< EFH = < EGH = 34\(^{\circ}\) (angles n the same segment)

< GHF = < GEF = 42\(^{\circ}\)(angles in the same segment)

< FOG = 42 + 34 = 76(exterior angle)

< FOG = < EOH = 76(vertically opposite angle)

< EDO = 90\(^{\circ}\), < DOE = \(\frac{76}{2}\) = 38\(^{\circ}\)

< HEG = 90\(^{\circ}\) - 38\(^{\circ}\) = 52\(^{\circ}\)


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Dicussion (1)

  • < EFH = < EGH = 34\(^{\circ}\) (angles n the same segment)

    < GHF = < GEF = 42\(^{\circ}\)(angles in the same segment)

    < FOG = 42 + 34 = 76(exterior angle)

    < FOG = < EOH = 76(vertically opposite angle)

    < EDO = 90\(^{\circ}\), < DOE = \(\frac{76}{2}\) = 38\(^{\circ}\)

    < HEG = 90\(^{\circ}\) - 38\(^{\circ}\) = 52\(^{\circ}\)

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