Question

In cyclic quadrilateral PQRS, angle S - angle Q = 80degree. Find angle S and angle Q​

Answer 1

$\underline { \blue { Cyclic \: Quadrilateral :}}$

If all the four vertices of a quadrilateral lie on the same circle is called Cyclic Quadrilateral .

$Here , \\ PQRS \: is \: a \: cyclic \: Quadrilateral .$

$and \: \angle S - \angle Q = 80\:degree \:--(1)$

$\angle S + \angle Q = 180\:degree \:--(2)$

$\pink { ( Pair \: of \: opposite \: angles \: of \: }$

$\pink{( a \: cyclic \: quadrilateral \: are}$

$\pink { supplementary )}$

/* Add equations (1) and (2) , we get */

$\implies 2\angle S = 260\degree$

$\implies \angle S = \frac{260\degree}{2} =130\degree$

$Put \: value \: of \: \angle S \: in \: eqution \:(2)\\,we \:get$

$\implies 130\degree + \angle Q = 180\degree$

$\implies \angle Q = 180\degree - 130\degree \\= 50\degree$

Therefore.,

$\red { \angle S } \green { = 130\degree }$

$\red { \angle R } \green { = 50\degree }$

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