Can someone help me solve for this angle?

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1 Answer
CW
Apr 28, 2018

#angleAFD=35^@#

Explanation:

enter image source here
Let #O# be the center of the circle.
#angleCAG=180-65-80=35^@#
#angleOCA=90-angleACG=90-65=25^@#
As #OA=OC, => angleOAC=angleOCA=25^@#
#=> angleFAB=90-angleOAC-angleCAG=90-25-35=30^@#
given #angleDOC=100^@#,
as #OD=OC, => angleODC=angleOCD=(180-100)/2=40^@#
#=> angleDCA=angleOCD+angleOCA=40+25=65^@#
As #ABCD# is a cyclic quadrilateral,
#=> angleDBA=angleDCA=65^@#
#=> angleABF=180-65=115^@#
Now consider #DeltaABF#,
#=> angleAFB=angleAFD=x=180-30-115=35^@#

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