Question

In the figure, $\angle BAD={78}^o,\angle DCF=x^{o}and\angle DEF=y^o.$ Find the values of x and y.

Answer 1

In the figure, two circles intersect each other at C and D.

$\angle BAD={78}^o,\angle DCF=x,\angle DEF=y$

ABCD is a cyclic quadrialteral.

$\therefore$ Ext. $\angle DCF=$ its interior opposite $\angle BAD$

$\Rightarrow x={78}^o$

In cyclic quadrilateral CDEF, $\angle DCF+\angle DEF={180}^o$

$\Rightarrow {78}^o+y={180}^o\Rightarrow y={180}^o-{78}^o$

$\Rightarrow y={102}^o$

Hence, $x={78}^o,andy={102}^o$