Question

please solve this.......​

Answer 1

Answer:

SO ,. <TQR= 15°...HOPE IT HELPS

Answer 2

Given:

PQRS is a square.

ΔSRT is an equilateral triangle.

To find:

∠TQR.

Solution:

PQRS is a square.

⇒ PQ = QR = RS = PS ➞ Relation(1)

(All 4 sides of a square are equal)

ΔTSR is an Equilateral triangle.

⇒ ST = TR = RS ➞ Relation(2)

(All 3 sides of an equilateral triangle are equal)

On observing 1, and 2 we see that they both are equal to RS.

⇒ PQ = QR = RS = PS = ST = TR. ➞ Relation(3)

From Relation(3):

⇒ TR = RQ

⇒ ∠QTR = ∠TQR

(Angles opposite to equal sides are equal)

Now, In ΔTRQ:

➞ ∠QTR + ∠TRQ + ∠TQR = 180° (ASP of a Δgle)

| We know that ∠TRQ = ∠TRS + ∠SRQ

➞ ∠QTR + ∠TRS + ∠SRQ + ∠TQR = 180°

| We know that ∠QTR = ∠TQR.

➞ ∠TQR + 60° + 90° + ∠TQR = 180°

➞2∠TQR + 150° = 180°

➞ 2∠TQR = 180° - 150°

➞ 2∠TQR = 30°

➞ ∠TQR = 30°/2

➞ ∠TQR = 15°

∴ Answer: ∠TQR = 15°.