In the diagram, EFGH is a cyclic quadrilateral in which EH || FG, EG and FH are chords. If < FHG = 424∘ ∘ and < EFH = 34∘

Assessment: JAMB UTME - Mathematics - 1999 Subject: General Mathematics

Question 1 Report

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

34

^{\circ}

42

^{\circ}

52

^{\circ}

76

^{\circ}

Answer Details

< 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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