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

JAMB 1999

In the diagram, EFGH is a cyclic quadrilateral in which EH || FG, EG, and FH are chords. If < FHG = 42º and < EFH = 34º, calculate < HEG.

A. 34^o
B. 42^o
C. 52^o
D. 76^o

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Correct Answer: Option C

Explanation

< EFH = < EGH = 34º (angles n the same segment)

< GHF = < GEF = 42º(angles in the same segment)

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

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

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

< HEG = 90º - 38º = 52º

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