In the given figure, PQRS is a square and ASMR is an equilateral triangle.​

2 thoughts on “In the given figure, PQRS is a square and ASMR is an equilateral triangle.​”

1. Step-by-step explanation:

   Solution:-

   Since PQRS is a square,

   angle PSR = angle QRS.. (each 90°)

   Now, again in equilateral triangle SRT,

   we have angle TSR = angle TRS …(each 60°)

   Angle PSR + Angle TSR = Angle QRS + Angle TRS

   ⇒ Angle TSP = Angle TRQ

   Now in Δ TSP and Δ TRQ, we have

   TS = TR (Sides of equilateral triangle)

   Angle TSP = Angle TRQ… (Proved above)

   PS = QR …(Sides of square)

   Δ TSP ≡ Δ TRQ

   So, PT = QT Proved.

   Now in Δ TQR, we have

   TR = QR ..(QR = RS = TR)

   Angle TQR = Angle QTR and Angle TQR + Angle QTR + Angle TRQ = 180°

   Angle TQR + Angle QTR + Angle TRS + Angle SRQ = 180°

   2(Angle TQR) + 60° + 90° = 180°..(∴ ∠ TQR = ∠ QTR)

   2(Angle TQR) = 180° – 150°

   2(Angle TQR) = 30°

   Angle TQR = 30/2

   Angle TQR = 15°

   Hence proved.

   keep smiling ☺️

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2. Answer:

   Good morning,

   Hope you will next mention what to do and what to find, the question which you gave just shares the info but it’s not mentioned that what we have to find.

   BTW, there is no such triangle with four sides, so the one you have mentioned is having four sides ‘ASMR’

   Step-by-step explanation:

   Hope You Understand

   Reply