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asked Jun 25, 2022 173k views

1 Answer

Aariba · Answer 1 · 2022-07-02T06:38:53+0000

Answer:

20°

Explanation:

In circle with center O, PS is diameter.

$m\angle PRS =90\degree$

(angle inscribed in semicircle)

PQRS is a cyclic quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

$\therefore m\angle QPS + m\angle QRS = 180\degree$

$\therefore (x\degree +25\degree) +(45\degree +90\degree) = 180\degree$

$\therefore x\degree +25\degree + 45\degree +90\degree = 180\degree$

$\therefore x\degree +160\degree = 180\degree$

$\therefore x\degree = 180\degree-160\degree$

$\huge\red {\therefore x\degree = 20\degree}$