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In the following diagram if AB=BC and CD=DE, find the value of Angle GCF?

Answer :: 45 degrees

solution ,, <BCA=a ,, <DCE=b

==<BGA=<CGF=90-a and similarly <DFE=<CFG=90-b

now in triangle CGF , <GCF=180-(90-a)-(90-b) <GCF=a+b

Also <BCD=90=2*(a+b) {given}

==<GCF=a+b=45

let BAC=a=BCA and DEC=DCE=b then CBG=(180-2a)-90=90-2a similarly CDF=90-2b this gives CGF=90-2a+a=90-a and similarly CFG=90-b also GCF=90-a-b . ......(1) from triangle GCF 90-a+90-b+90-a-b=180 or a+b=45 substitute in (1) angle GCF=45

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