In the figure, $\angle BAD = 78^o, \angle DCF = x^o$ and $\angle DEF = y^o$. Find the values of $x$ and $y$.
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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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Updated on: 10-Oct-2022

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