ABCDE is a regular pentagon. if AB and DC are produced to meet F,Find the value of BFC
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Given : ABCDE is a regular pentagon
AB and DC are produced to meet F
To Find : the value of ∠BFC
Solution:
ABCDE is a regular pentagon
∠ABC = 108°
∠BCD = 108°
ABF is straight line
∠ABC + ∠CBF = 180°
=> 108° + ∠CBF = 180°
=> ∠CBF = 72°
DCF is straight line
∠DCB + ∠BCF = 180°
=> 108° + ∠BCF = 180°
=> ∠BCF = 72°
in Δ BCF
∠CBF + ∠BCF + ∠BFC = 180°
=> 72° + 72° + ∠BFC = 180°
=> ∠BFC = 36°
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