Question

In a square $PQRS$, an equilateral triangle $△TQR$ is formed, then $m\angle PTS$- ?

• A. ${75}^o$
• B. ${90}^o$
• C. ${120}^o$
• D. ${150}^o$

Answer 1

The correct option is D ${150}^o$

$PQ=QR=RS=SP=QT=TR$

Angle opposite to equal sides are equal.

$\angle QTP=\angle QPT=x$

In triangle $QTP\Rightarrow 30+x+x=180$

$\Rightarrow x=75$

$\angle RTS=\angle RST=y$

In triangle$RST\Rightarrow 30+y+y=180$

$\Rightarrow y=75$

$\angle QRT+\angle RTS+\angle PTS+\angle PTQ=360$

$\angle 60+\angle 75+\angle 75+\angle PTQ=360$

$\angle PTS={150}^0$