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Question

Find the relation between the angles X and Y.

A
Y=180oX
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B
Y=90oX
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C
They are supplementary angles.
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D
Nothing cannot be said without sufficient data.
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Solution

The correct option is C They are supplementary angles.
XYVW is a quadrilateral formed by intersections of two circles.
Connect the intersection points of the two circles.
XABW is a cyclic quadrilateral to the smaller circle.
As opposite angles of a cyclic quadrilateral have a sum of 180o,
ABW=180oX

WBV is a straight line.
ABV=180oABW
ABV=180o(180oX)=X

AYVB is a cyclic quadrilateral to the larger circle.
Y=180oABV
Y=180oX
Y+X=180o

X and Y are supplementary angles.

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