Question

PQRS is a square and PQT is an equilateral triangle on the side PQ of the
square, angle SPT= -----
a)45° b) 40° c) 30° d) 15°

Answer 1

Answer:

Because PQRS is a square

∠PSR=∠QRS=90

∘

Now In △SRT

∠TSR=∠TRS=60

∘

∠PSR+∠TSR=∠QRS+∠TRS

⟹∠TSP=∠TRQ

Now in △TSP and △TRQ

TS=TR

∠TSP=∠TRQ

PS=QR

Therefore , △TSP≡△TRQ

So PT=QT

(ii) Now in △TQR,

TR=QR(RQ=SR=TR)

∠TQR=∠QTR

And ∠TQR+∠QTR+∠TRQ=180

⟹∠TQR+∠QTR+∠TRS+∠SRQ=180

⟹2(∠TQR)+60+90=180 (∠TQR=∠QTR)

2(∠TQR)=30

⟹∠TQR=15

∘

Answer 2

Question :

PQRS is a square and PQT is an equilateral triangle on the side PQ of the square , angle SPT =

a) 45°

b) 40°

c) 30°

d) 15°

Answer :

c) 30°