question_answer

An equilateral \[\Delta TQR\]is drawn inside a square PQRS. The value of the angle PTS, in degrees) is

[SSC (10+2) 2012]

A) 120                              

B) 150   

C) 75                                

D) 90

Correct Answer: B

Solution :

Since, \[\Delta TQR\]is an equilateral triangle.

\[\therefore \]\[\angle TQR=\angle TRQ=\angle RTQ=60{}^\circ \]

and       \[TQ=TR=RQ\]

and       \[SR=RQ=PQ=SP\][sides of square]

Now, in \[\Delta RTS\]

\[RT=SR\]

\[\therefore \]      \[\angle STR=RST\]

(angle opposite to equal sides are equal]

\[=\frac{180{}^\circ -30{}^\circ }{2}=75{}^\circ \]

Similarly, in \[\Delta QTP,\]\[QT=PQ\]

\[\angle PTQ=\angle QPT=75{}^\circ \]

Now, at point T

\[\angle PTS+\angle PTQ+\angle QTR+\angle RTS=360{}^\circ \]

[since, angles around on point is equal to \[360{}^\circ \]]

\[\Rightarrow \]\[\angle PTS=360{}^\circ -\,\,(75{}^\circ +60{}^\circ +75{}^\circ )\]

\[=360{}^\circ -210{}^\circ =150{}^\circ \]