Question

A regular pentagon ABCDE and a square ABFG are formed on opposite sides of AB. Find ∠BCF​

Answer 1

Answer:

ABCDE is a regular pentagon and ABFG is a square.

So the sides of pentagon and square are equal.

Each angle of square = 90°

Each angle of regular pentagon = 108°

From the figure <FBC =360 - [<ABF + <ABC]

<FBC = 360 - (90 +108 ) =360 - 198 = 162°

<BFC = <BCF (since BF = BC, Δ BCF isosceles triangle )

<BCF= 1/2(180 - 162) =9°

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