A) \[{{70}^{o}}\]
B) \[{{50}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{80}^{o}}\]
Correct Answer: C
Solution :
\[\angle ROQ=\angle SOP={{60}^{o}}\] ?(i) [Vertically opposite angles] \[\therefore \]\[PR=SQ\Rightarrow PO=SO\] (Diagonals of a rectangle are equal and bisect each other) \[\Rightarrow \]\[\angle OPS=\angle OSP\] [\[\because \]In a triangle, angles opposite to equal sides are equal] In \[\Delta POS,\]by angle sum property \[\angle OSP+\angle OPS+\angle SOP={{180}^{o}}\] \[\Rightarrow \]\[2\angle OSP={{180}^{o}}-{{60}^{o}}\][Using (i) & (ii)] \[\Rightarrow \]\[\angle OSP={{60}^{o}}\]You need to login to perform this action.
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