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AB and BC are the sides of a regular pentagon. CD and DE are the sides of a regular hexagon. If OB and OD are the angle bisectors of ABC and CDE, and BOD=126, then find the measure of BCD.

A
60
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B
120
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C
100
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D
80
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Solution

The correct option is B 120

AB and BC are the sides of regular pentagon

ABC=(52)×1805=108

Each angle of a regular polygon
=(n2)×180n
OBC=ABC2=54

Similarly,
BCD=(62)×1806=120
ODC=BCD2=60

Now,
OBC+ODC+BOD+BCD=360
[Sum of all the angles of a quadrilateral =360]

54+60+126+BCD=360

BCD=360(54+60+126)

BCD=120

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