Question

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

Answer 1

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

Answer 2

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