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MATHEMATICS

JAMB 2020 - Question 28

Mathematics 2020 JAMB Past Questions - Question 28: in the diagram above, EFGH is a cyclic quadrilateral in which EH||FG, EG and FH are chords. if Ë‚FGH = 42° and Ë‚ EFG = 34° calculate Ë‚ HEG

Use the diagram to answer question that follows

in the diagram above, EFGH is a cyclic quadrilateral in which EH||FG, EG and FH are chords. if Ë‚FGH = 42° and Ë‚ EFG = 34° calculate Ë‚ HEG

A: 34°

B: 42°

C: 52°

D: 76°

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Correct Answer

Explanation

EGH = 34° = EFH ( Angles in the same segment) i.e HJG = 180 – (42° + 34°) = 104° (sum of angles in a Δ ) HJE° = 76° (Angles on a straight line ) i.e (180 – 104) = 76â�° But Δ HJE is an Δ HEG =HFG (alternate angles) i.e HEG = FGE = EHF = HEG i.e HEG = 180 -76° HEG = EHJ (iso . Δ) EHJ + HEG = 180 76° (sum of angles in a Δ) = 104 i.e HEG = 104 /2 = 52°