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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