In the figure, $\angle BAD = 78^o, \angle DCF = x^o$ and $\angle DEF = y^o$. Find the values of $x$ and $y$.
"
Given:
$\angle BAD = 78^o, \angle DCF = x^o$ and $\angle DEF = y^o$.
To do:
We have to find the values of $x$ and $y$.
Solution:
In the given figure, two circles intersect each other at $C$ and $D$.
$\angle BAD = 78^o, \angle DCF = x, \angle DEF = y$
$ABCD$ is a cyclic quadrilateral.
$\angle DCF = interior\ opposite\ \angle BAD$
$x = 78^o$
In cyclic quadrilateral $CDEF$,
$\angle DCF + \angle DEF = 180^o$
$78^o + y = 180^o$
$y = 180^o - 78^o$
$y = 102^o$
Hence $x = 78^o$ and $y = 102^o$.
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