In the given figure ΔBAC = ΔQRP by SAS criterion of congruence. Find the value of x and y.

Given: ΔBAC = ΔQRP (By SAS rule)

So, BA = QR

⇒ 3x + 10 = 5y + 15 ……(i)

∠BAC = ∠QRP

⇒ 2x + 15° = 5x – 60° ……(ii)

From eq. (ii), we have

2x + 15 = 5x – 60

⇒ 2x – 5x = -15 – 60

⇒ -3x = -7 5

⇒ x = 25

From eq. (i), we have

3x + 10 = 5y + 15

⇒ 3 × 25 + 10 = 5y + 15

⇒ 75 + 10 = 5y + 15

⇒ 85 = 5y + 15

⇒ 85 – 15 = 5y

⇒ 70 = 5y

⇒ y = 14

Hence, the required values of x and y are 25 and 14 respectively.